Search

We have developed a thermodynamic theory in the non-equilibrium regime, which we describe as a thermodynamic system–bath model [Koyanagi and Tanimura, J. Chem. Phys. 160, 234112 (2024)]. Based on the dimensionless (DL) minimum work principle, non-equilibrium thermodynamic potentials are expressed in terms of non-equilibrium extensive and intensive variables in time derivative form. This is made possible by incorporating the entropy production rate into the definition of non-equilibrium thermodynamic potentials. These potentials can be evaluated from the DL non-equilibrium-to-equilibrium minimum work principle, which is derived from the principle of DL minimum work and is equivalent to the second law of thermodynamics. We thus obtain the non-equilibrium Massieu–Planck potentials as entropic potentials and the non-equilibrium Helmholtz–Gibbs potentials as free energies. Unlike the fluctuation theorem and stochastic thermodynamics theory, this theory does not require the assumption of a factorized initial condition and is valid in the full quantum regime, where the system and bath are quantum mechanically entangled. Our results are numerically verified by simulating a thermostatic Stirling engine consisting of two isothermal processes and two thermostatic processes using the quantum hierarchical Fokker–Planck equations and the classical Kramers equation derived from the thermodynamic system–bath model. We then show that, from weak to strong system–bath interactions, the thermodynamic process can be analyzed using a non-equilibrium work diagram analogous to the equilibrium one for given time-dependent intensive variables. The results can be used to develop efficient heat machines in non-equilibrium regimes. [ABSTRACT FROM AUTHOR]

We developed a computer code for the thermodynamic quantum Fokker–Planck equations (T-QFPE), derived from a thermodynamic system–bath model. This model consists of an anharmonic subsystem coupled to multiple Ohmic baths at different temperatures, which are connected to or disconnected from the subsystem as a function of time. The code numerically integrates the T-QFPE and their classical expression to simulate isothermal, isentropic, thermostatic, and entropic processes in both quantum and classical cases. The accuracy of the results was verified by comparing the analytical solutions of the Brownian oscillator. In addition, we illustrated a breakdown of the Markovian Lindblad-master equation in the pure quantum regime. As a demonstration, we simulated a thermostatic Stirling engine employed to develop non-equilibrium thermodynamics [S. Koyanagi and Y. Tanimura, J. Chem. Phys. 161, 114113 (2024)] under quasi-static conditions. The quasi-static thermodynamic potentials, described as intensive and extensive variables, were depicted as work diagrams. In the classical case, the work done by the external field is independent of the system–bath coupling strength. In contrast, in the quantum case, the work decreases as the coupling strength increases due to quantum entanglement between the subsystem and bath. The codes were developed for multicore processors using Open Multi-Processing (OpenMP) and for graphics processing units using the Compute Unified Device Architecture. These codes are provided in the supplementary material. [ABSTRACT FROM AUTHOR]

We present a dynamic density functional theory for modeling the effects of applied electric fields on the local structure of polymers with added salt (polymer electrolytes). Time-dependent equations for the local electrostatic potential and volume fractions of polymer, cation, and anion of added salt are developed using the principles of linear irreversible thermodynamics. For such a development, a field theoretic description of the free energy of polymer melts doped with salts is used, which captures the effects of local variations in the dielectric function. Connections of the dynamic density functional theory with experiments are established by relating the three phenomenological Onsager's transport coefficients of the theory to the mutual diffusion of electrolyte, ionic conductivity, and transference number of one of the ions. The theory is connected with a statistical mechanical model developed by Bearman and Kirkwood [J. Chem. Phys. 28, 136 (1958)] after relating the three transport coefficients to friction coefficients. The steady-state limit of the dynamic density functional theory is used to understand the effects of dielectric inhomogeneity on the phase separation in polymer electrolytes. The theory developed here provides not only a way to connect with experiments but also to develop multi-scale models for studying connections between local structure and ion transport in polymer electrolytes. [ABSTRACT FROM AUTHOR]

We formulate a thermodynamic theory applicable to both classical and quantum systems. These systems are depicted as thermodynamic system–bath models capable of handling isothermal, isentropic, thermostatic, and entropic processes. Our approach is based on the use of a dimensionless thermodynamic potential expressed as a function of the intensive and extensive thermodynamic variables. Using the principles of dimensionless minimum work and dimensionless maximum entropy derived from quasi-static changes of external perturbations and temperature, we obtain the Massieu–Planck potentials as entropic potentials and the Helmholtz–Gibbs potentials as free energy. These potentials can be interconverted through time-dependent Legendre transformations. Our results are verified numerically for an anharmonic Brownian system described in phase space using the low-temperature quantum Fokker–Planck equations in the quantum case and the Kramers equation in the classical case, both developed for the thermodynamic system–bath model. Thus, we clarify the conditions for thermodynamics to be valid even for small systems described by Hamiltonians and establish a basis for extending thermodynamics to non-equilibrium conditions. [ABSTRACT FROM AUTHOR]

Due to their potential applications in energy production based on waste heat, direct solar radiation or other energy sources, semiconductor materials have for years attracted the attention of theoretical and experimental researchers. The focus has been on improving the performance of thermoelectric devices through several strategies and special interest has been placed on materials with spatially inhomogeneous transport properties. Inhomogeneity can be achieved in various ways, all of them leading, to a greater or lesser extent, to an improvement of the thermoelectric performance. In this paper, general linear heat and electric charge transport processes in inhomogeneous materials are addressed. The guiding idea followed here is that there exists a relationship between inhomogeneity (structuring), minimum entropy production and performance which may be fruitfully exploited for designing more efficient thermoelectric semiconductor devices. We first show that the stationary states of such materials are minimum global entropy production states. This constitutes an extension of the validity of Prigogine's minimum entropy principle. The heat and charge transport equations obtained within the framework of classical irreversible thermodynamics are solved to find the stationary profiles of temperature and self-consistent electric potential in a one-dimensional model of a silicon–germanium alloy subjected to an external temperature difference. This allows us to assess the effect of the spatial inhomogeneity on the thermoelectric performance. We find that, regardless of the value of the applied temperature difference, the system may efficiently operate in a regime of minimum entropy production and high efficiency. [ABSTRACT FROM AUTHOR]

Equilibrium thermodynamics describes the energy exchange of a body with its environment. Here, we describe the global energy exchange of an ideal gas in the Coutte flow in a thermodynamic-like manner. We derive a fundamental relation between internal energy as a function of parameters of state. We analyze a non-equilibrium transition in the system and postulate the extremum principle, which determines stable steady states in the system. The steady-state thermodynamic framework resembles equilibrium thermodynamics. [ABSTRACT FROM AUTHOR]

The understanding of neural excitability and oscillations in single neuron dynamics remains incomplete in terms of global stabilities and the underlying mechanisms for phase formation and associated phase transitions. In this study, we investigate the mechanism of single neuron excitability and spontaneous oscillations by analyzing the potential landscape and curl flux. The topological features of the landscape play a crucial role in assessing the stability of resting states and the robustness/coherence of oscillations. We analyze the excitation characteristics in Class I and Class II neurons and establish their relation to biological function. Our findings reveal that the average curl flux and associated entropy production exhibit significant changes near bifurcation or phase transition points. Moreover, the curl flux and entropy production offer insights into the dynamical and thermodynamical origins of nonequilibrium phase transitions and exhibit distinct behaviors in Class I and Class II neurons. Additionally, we quantify time irreversibility through the difference in cross-correlation functions in both forward and backward time, providing potential indicators for the emergence of nonequilibrium phase transitions in single neurons. [ABSTRACT FROM AUTHOR]

We discuss non-equilibrium thermodynamics of the mean-field Ising model from a geometric perspective, focusing on the thermodynamic limit. When the number of spins is finite, the Gibbs equilibria form a smooth Legendrian submanifold in the thermodynamic phase space whose points describe the stable macroscopic states of the system. We describe the convergence of these smooth Legendrian submanifolds, as the number of spins goes to infinity, to a singular Legendrian submanifold, admitting an analytic continuation that contains both the stable and metastable states. We also discuss the relaxation to a Gibbs equilibrium when the physical parameters are changed abruptly. The relaxation is defined via the gradient flow of the free energy with respect to the Wasserstein metric on microscopic states, that is, in the geometric language, via the gradient flow of the generating function of the equilibrium Legendrian with respect to the ghost variables. This leads to a discrete Fokker-Planck equation when the number of spins is finite. We show that in the thermodynamic limit this description is closely related to the seminal model of relaxation proposed by Glauber. Finally, we find a special range of parameters where such relaxation happens instantaneously, along the Reeb chords connecting the initial and the terminal Legendrian submanifolds. [ABSTRACT FROM AUTHOR]

We study the issue of temperature in a steady system around a black hole event horizon, contrasting it with the appearance of divergence in a thermal equilibrium system. We focus on a spherically symmetric system governed by general relativity, particularly examining the steady state with radial heat conduction. Employing an appropriate approximation, we derive exact solutions that illuminate the behaviors of number density, local temperature, and heat in the proximity of a black hole. We demonstrate that a carefully regulated heat inflow can maintain finite local temperatures at the black hole event horizon, even without considering the back-reaction of matter. This discovery challenges conventional expectations that the local temperature near the event horizon diverges in scenarios of thermal equilibrium. This implications shows that there's an intricate connection between heat and gravity in the realm of black hole thermodynamics. [ABSTRACT FROM AUTHOR]

The spatiotemporally-nonlocal phenomena in heat conduction become significant but challenging for metamaterials with artificial microstructures. However, the microstructure-dependent heat conduction phenomena are captured under the hypothesis of spatiotemporally local equilibrium. To capture the microstructure-dependent heat conduction phenomena, a generalized nonlocal irreversible thermodynamics is proposed by removing both the temporally-local and spatially-local equilibrium hypotheses from the classical irreversible thermodynamics. The generalized nonlocal irreversible thermodynamics has intrinsic length and time parameters and thus can provide a thermodynamics basis for the spatiotemporally-nonlocal law of heat conduction. To remove the temporally-local equilibrium hypothesis, the generalized entropy is assumed to depend not only on the internal energy but also on its first-order and high-order time derivatives. To remove the spatially local equilibrium hypothesis, the thermodynamics flux field in the dissipation function is assumed to relate not only to the thermodynamics force at the reference point but also to the thermodynamics force of the neighboring points. With the developed theoretical framework, the thermodynamics-consistent spatiotemporally-nonlocal models can then be developed for heat transfer problems. Two examples are provided to illustrate the applications of steady-state and transient heat conduction problems. [ABSTRACT FROM AUTHOR]

This paper is devoted to presenting a micromechanical model for describing instantaneous and long-term mechanical behaviors of typical quasi-brittle rocks under lateral unloading conditions. The unified damage-friction coupling model is formulated in a combined linear homogenization and irreversible thermodynamics framework. Crack propagation and friction sliding are regarded as the two primary dissipation and coupling mechanisms, respectively related to material damage and plastic deformation. Rock damage due to microcracking is divided into two parts: an instantaneous part induced by variation in stresses and a time-dependent part caused by subcritical extension of microcracks due to stress corrosion. Both the instantaneous and long-term mechanical behaviors of rock are taken into account in a unified way, which closely resemble the excavation scenarios encountered in practical engineering. In addition, we conduct a series of experiments under unloading conditions to provide experimental data for model validation and analytical predictions. Highlights: A unified micromechanical model is presented to characterize the instantaneous and long-term mechanical responses under various loading and unloading stress paths. Short- and long-term mechanical behaviors of red sandstone under unloading conditions are investigated experimentally. Damage-controlled and time-controlled algorithms are provided to perform the numerical simulation. [ABSTRACT FROM AUTHOR]

In the past 20 years, active matter has been a very successful research field, bridging the fundamental physics of nonequilibrium thermodynamics with applications in robotics, biology, and medicine. Active particles, contrary to Brownian particles, can harness energy to generate complex motions and emerging behaviors. Most active-matter experiments are performed with microscopic particles and require advanced microfabrication and microscopy techniques. Here, we propose some macroscopic experiments with active matter employing commercially available toy robots (the Hexbugs). We show how they can be easily modified to perform regular and chiral active Brownian motion and demonstrate through experiments fundamental signatures of active systems such as how energy and momentum are harvested from an active bath, how obstacles can sort active particles by chirality, and how active fluctuations induce attraction between planar objects (a Casimir-like effect). These demonstrations enable hands-on experimentation with active matter and showcase widely used analysis methods. Editor's Note: Active matter consists of particles (e.g., birds, cells, or synthetic objects) that can self-propel. These systems are currently being researched not only because they can display collective behaviors and some level of self-organization but also because of their potential applications such as in drug delivery. Both in the classroom and in research labs, toy robots such as Hexbugs can be used to model active matter. This article shows that, by playing with these toys, undergraduate students can visualize the concepts they're being taught in advanced thermodynamics or soft matter classes: chiral and non-chiral active Brownian motion, interaction of the particles with their environment, and particle sorting. Time to play! [ABSTRACT FROM AUTHOR]

An analogy is drawn between version of non-equilibrium thermodynamics a distribution-based containing an additional thermodynamic first-passage time parameter, nonequilibrium statistical operator method and extended irreversible thermodynamics with flows as an additional thermodynamic parameter. Thermodynamics containing an additional thermodynamic first-passage time parameter maps to extended irreversible thermodynamics. Various conditions for the dependence of the distribution parameters of the first-passage time on the random value of energy, the first thermodynamic parameter, are considered. Time parameter relaxation time τ of extended irreversible thermodynamics is replaced by the average first-passage time. Expressions are obtained for the thermodynamic parameter, the conjugate of the first passage time through the entropy change, and for the average first passage time through the flows. [ABSTRACT FROM AUTHOR]

A new variational theory of the growth of particles of a new phase in supercooled multicomponent melts is developed. The crystallization of supercooled metal melts is characterized by various nonlinear effects on the surface of a growing crystal. A new variational means of nonequilibrium thermodynamics is developed to consider such effects, based on the principle of minimum entropy production. The approach allows the growth of an embryo of a new phase to be considered by allowing for the interrelated influence of thermal and diffusion processes, along with non-stationary effects associated with deviations from the local equilibrium on the surface of the growing embryo. The transfer of components across the phase boundary is described in the form of chemical reactions. An advantage of the theory is the possibility of obtaining a generalized theoretical description of nonlinear effects on the crystal's surface. Expressions of crystal growth are given for different types of multicomponent metal systems to demonstrate the use of the approach. [ABSTRACT FROM AUTHOR]

Irreversible entropy production (IEP) plays an important role in the field of quantum thermodynamics. In the present work, we investigate the geometrical bounds of IEP in nonequilibrium thermodynamics by exemplifying a two-qubit system coupled to three noise channels, including amplitude damping channel, phase damping channel, and depolarizing channel, respectively. We find that the geometrical bounds of the IEP always shift in an identical way, namely, only the upper bound becomes tighter under phase damping channel and depolarizing channel, respectively, in the presence of correlation effect of the noise channel. However, both the lower bound and the upper bound turn to be tighter in the situation of amplitude damping channel in the presence of correlation effect of the noise channel. By harvesting the benefits of correlation effect of noise channel and the entanglement between two qubits, the values of the IEP, quantifying the degree of thermodynamic irreversibility, could be suppressed in a controllable manner. Our results are expected to deepen our understanding of the nature of irreversibility under ambient conditions. [ABSTRACT FROM AUTHOR]

In this study, the transported entropy of ions for 8YSZ and 10Sc1CeSZ electrolytes was experimentally determined to enable precise modeling of heat transport in solid oxide cells (SOCs). The Peltier coefficient, crucial for thermal management, was directly calculated, highlighting reversible heat transport effects in the cell. While data for 8YSZ are available in the literature, providing a basis for comparison, the results for 10Sc1CeSZ show slightly smaller Seebeck coefficients but higher transported ion entropies. Specifically, at 700 ° C and an oxygen partial pressure of p O 2 = 0.21 bar, values of S O 2 − * = 52 ± 10 J/K·F for 10Sc1CeSZ and S O 2 − * = 48 ± 9 J/K·F for 8YSZ were obtained. The transported entropy was also validated through theoretical calculations and showed minimal deviations when comparing different cell operation modes (O2||O2−||O2 and H2, H2O||O2−||O2). The influence of the transported entropy of the ions on the total heat generation and the partial heat generation at the electrodes is shown. The temperature has the greatest influence on heat generation, whereby the ion entropy also plays a role. Finally, the Peltier coefficients of 8YSZ for all homogeneous phases agree with the literature values. [ABSTRACT FROM AUTHOR]

In a multivariable system, there are usually a number of relaxation times. When some of the relaxation times are shorter than others, the corresponding variables will decay to their equilibrium value faster than the others. After the fast variables have decayed, the system can be described with a smaller number of variables. From the theory of nonequilibrium thermodynamics, as formulated by Onsager, we know that the coefficients in the linear flux–force relations satisfy the so-called Onsager symmetry relations. The question we will address in this paper is how to eliminate the fast variables in such a way that the coefficients in the reduced description for the slow variables still satisfy the Onsager relations. As the proof that Onsager gave of the symmetry relations does not depend on the choice of the variables, it is equally valid for the subset of slow variables. Elimination procedures that lead to symmetry breaking are possible, but do not consider systems that satisfy the laws of nonequilibrium thermodynamics. [ABSTRACT FROM AUTHOR]

An extension and further development of our previous article [J. Non-equilibrium Thermodyne. 37 (2012), 119–141] is presented. We study the irreversible non-equilibrium thermodynamics (INT) properties of the exact solution to the dilute homogeneously charged gas problem with unsteady Rayleigh flow. In contrast to previous research, the charged gas flows under the influence of an external force, the flat plate oscillates, and the displacement current term is considered, leading to significant advancements in understanding natural plasma dynamics. We are solving the Boltzmann kinetic equation (BKE) Krook model supplemented by Maxwell's equations. We used a travelling wave and moments method with an electron velocity distribution function (EVDF). To the best of our knowledge, as three new scientific achievements, we introduced a new mathematical model for calculating the thermodynamic forces, kinetic coefficients, and fluxes variables, Equations (28–40) and (50–54). Second, we determined, with reasonable accuracy, the thermodynamic equilibrium time of electrons, tequ = 26.7955, under an external force. We clarify the difference between equilibrium EVDF and perturbed EVDF and take advantage of BKE to account for non-equilibrium thermodynamic principles. For diamagnetic and paramagnetic plasmas, the extended Gibbs equation predicts ratios between various contributions to the internal energy change (IEC) is presented. A standard laboratory argon plasma model is used to apply the results. [ABSTRACT FROM AUTHOR]

The interaction between water motion efficiency, outlet control mechanisms, and energy dynamics management hinges significantly on turbulence characteristics. However, understanding the influence of input velocities and duct features on outlets remains elusive. This study employs the realizable k − ɛ viscous model and Reynolds-averaged Navier–Stokes equations (RANS equations) to explore transient water dynamics encountering a cold front through ducts leading to convergence or divergence. Using Ansys Fluent 2023R2 and the waterlight workflow, meticulous meshing of the ducts is executed to capture flow intricacies accurately. Grid independence, suitable boundary conditions, and solver settings are carefully considered to ensure reliable results for investigating four key research questions. Duct bending introduces non-uniformities in velocity distribution, impacting exit velocity and altering flow characteristics and turbulence. In Case III, centrifugal forces from a 90° bend result in higher outlet velocities at the convergent exit and secondary flow patterns like swirls and vortexes. Additionally, entrance velocities influence Reynolds numbers, affecting mixing, heat transfer coefficients, and flow regimes, thereby optimizing thermal conductivity. This comprehensive investigation sheds light on optimizing water dynamics and energy management across various duct configurations, offering valuable insights into efficient flow control and thermal performance enhancement. [ABSTRACT FROM AUTHOR]

From a finite-time thermodynamics perspective, a thermoeconomic analysis of a Novikov model employing a linear heat transfer law is carried out. A new component in the cost function is proposed to examine its relationship with waste management while operating in the maximum power, ecological, and efficient power regimes. The methodology consists of optimizing the profit function by including our new waste management cost function, leveraging the same method used by DeVos ("Endoreversible thermoeconomics," Energy Convers. Manage., vol. 36, pp. 1–5, 1995) and Pacheco et al. ("Thermoeconomic optimization of an irreversible novikov plant model under different regimes of performance," Entropy, vol. 19, p. 118, 2017). Searching for the optimal thermoeconomic efficiencies for the ecological case a novel numerical method developed by the corresponding author (A. M. Ares de Parga-Regalado, "Analytical approximation of optimal thermoeconomic efficiencies for a novikov engine with a Stefan–Boltzmann heat transfer law," Results Phys., 2023) is used. Analytical expressions for the optimal efficiencies are obtained, and the impact of the proposed term on these values is investigated. [ABSTRACT FROM AUTHOR]

Evolution requires selection. Molecular/chemical/preDarwinian evolution is no exception. One molecule must be selected over another for molecular evolution to occur and advance. Evolution, however, has no goal. The laws of physics have no utilitarian desire, intent or proficiency. Laws and constraints are blind to "usefulness." How then were potential multi-step processes anticipated, valued and pursued by inanimate nature? Can orchestration of formal systems be physico-chemically spontaneous? The purely physico-dynamic self-ordering of Chaos Theory and irreversible non-equilibrium thermodynamic "engines of disequilibria conversion" achieve neither orchestration nor formal organization. Natural selection is a passive and after-the-fact-of-life selection. Darwinian selection reduces to the differential survival and reproduction of the fittest already-living organisms. In the case of abiogenesis, selection had to be 1) Active, 2) Pre-Function, and 3) Efficacious. Selection had to take place at the molecular level prior to the existence of non-trivial functional processes. It could not have been passive or secondary. What naturalistic mechanisms might have been at play? [ABSTRACT FROM AUTHOR]

Films that develop compositional heterogeneity during drying offer a promising approach for achieving tailored functionalities. These functionalities can be realized by strategically directing different components during the drying process. One approach to achieve this is through spontaneous size segregation of colloidal particles. Two variants thereof have previously been observed in binary suspensions: layer formation (self-stratification) due to kinetically driven concentration gradients, and micro-domain formation (phase separation) due to thermodynamic depletion interactions between the small and large species. Surprisingly, in the context of binary colloidal films, these phenomena have never been investigated concurrently during evaporation. We show how we can achieve both self-stratification and domain formation in a single step. Using real-time 3D confocal fluorescence microscopy, we quantitatively unravel the effects of various parameters on the emergence of compositional heterogeneity. We reveal that beyond a certain size ratio, micro-phase separation becomes a prominent mechanism dictating the final morphology. The initial volume fraction minimally affects the final domain size but significantly impacts self-stratification. Reducing the evaporation rate increases the domain size while minimizing stratification. Finally, reducing the colloidal electrostatic interaction by a small increase in salt concentration enhances phase separation yet reverses stratification. These findings unveil a strategy for harnessing two distinct size segregation mechanisms in a single film, forming a foundation for customizable self-partitioning coatings.   • In-situ confocal imaging unravels the drying of a binary colloidal film. • Self-stratification and phase separation occur simultaneously during drying. • Initial volume fractions, evaporation rate, and salt concentration govern demixing. • Drying binary dispersions demonstrate great potential for self-organizing coating. [ABSTRACT FROM AUTHOR]

Recent experiments suggest that mesoscale catalysts are active materials that power their motion with chemical free energy from their environment and also "chemotax" with respect to substrate gradients. In the present work, we explore a thermodynamic framework for relating this chemotaxis to the evolution of a system down the gradient of its free energy. This framework builds upon recent studies that have employed the Wasserstein metric to describe diffusive processes within the Onsager formalism for irreversible thermodynamics. In this work, we modify the Onsager dissipation potential to explicitly couple the reactive flux to the diffusive flux of catalysts. The corresponding gradient flow is a modified reaction-diffusion equation with an advective term that propels the chemotaxis of catalysts with the free energy released by chemical reactions. In order to gain first insights into this framework, we numerically simulate a simplified model for spherical catalysts undergoing artificial chemotaxis in one dimension. These simulations investigate the thermodynamic forces and fluxes that drive this chemotaxis, as well as the resulting dissipation of free energy. Additionally, they demonstrate that chemotaxis can delay the relaxation to equilibrium and, equivalently, prolong the duration of nonequilibrium conditions. Although future simulations should consider a more realistic coupling between reactive and diffusive fluxes, this work may provide insight into the thermodynamics of artificial chemotaxis. More generally, we hope that this work may bring attention to the importance of the Wasserstein metric for relating nonequilibrium relaxation to the thermodynamic free energy and to large deviation principles. [ABSTRACT FROM AUTHOR]

The realization of nanoscale devices largely depends on our ability to control and manipulate interfacial interactions and, thus, understanding of the mechanisms of surface/interface instabilities. In this work, theoretically as well as technologically important and distinct two thermodynamic systems, which are exposed to (isobaric) and isolated from (isochoric) external body forces and surface tractions, are formulated by using irreversible thermodynamics in combination with the generalized variational method. The starting point for the present formulation closely follows up the Fowler and Guggenheim [Statistical Thermodynamics (University Press, Cambridge, 1952)] interpretation of the Planck inequality [Über Prinzip Vermehrung Entropie: Ann. Phys. Series 2(32), 462 (1887)] for isothermal reversible and irreversible (natural) infinitesimal changes in heterogeneous systems (multi-phase and multi-component). By combining this fundamental principle with the interlink between the dissipation function and global internal entropy production postulates, two distinct sets of governing equations for the surface drift-diffusion flux as well as the rate of evaporation/condensation and/or the growth/recrystallization of amorphous solid thin films are obtained for isochoric and isobaric systems. The role of Eshelby's energy-momentum tensor in the generalized potential for the interface displacement is found to differ (opposite in sign) for isochoric and isobaric systems. To demonstrate the importance of these sign conflicts, two sets of computer experiments are performed on isochoric and isobaric systems. They showed us that the elastic strain energy density contribution to the generalized driving force for surface drift-diffusion alone favoring flat and smooth surfaces in isobaric systems regardless of the sign of the uniaxial stress (healing), rather than causing the surface roughness and even catastrophic crack initiation as the case in internally strained isochoric systems. Computer simulations allowed us to track down the dynamical behavior of test modules by furnishing surface and strain energy variations, combined with the Global Helmholtz free change, which indicates the existence of two regimes: initial smooth surface undulations followed up by the rather chaotic crack formation and propagation stage at the middle of the thin film supported by the stiff substrate. In this study, we mainly focused on the development kinetics of "Stranski–Krastanow" island-type morphology, initiated by the nucleation route rather than the surface roughening scheme. The physicomathematical model, which is based on the irreversible thermodynamics treatment of surfaces and interfaces with singularities [T. O. Ogurtani, J. Chem. Phys. 124, 144706 (2006)], furnishes us to have autocontrol on otherwise free-motion of the triple junction contour line between the substrate and the droplet without presuming any equilibrium dihedral contact (wetting) angles at edges. We have also demonstrated the formation of the Stranski–Krastanow (SK)-type doublet islanding (quantum dots) as a stationary nonequilibrium state in an epitaxially strained thin flat droplet on a rigid substrate by introducing the wetting potential—invoked by the quantum confinement—into the scenario and carefully selecting the system parameters (size and shape) for the isochoric system represented by [Ge/Si (100)]. It has been also shown that on the contrary to common perceptions, the Stranski–Krastanow islands are in genuine stationary nonequilibrium states in the sense of Prigogine if one invokes proper free-moving boundary conditions at triple junctions deduced from the irreversible thermodynamics rather than ad hoc periodic or reflecting constrains at the edges. [ABSTRACT FROM AUTHOR]

A novel modeling and new irreversibility analysis of non-homogeneous charged gas flow is presented as an extension and further development of our previous article [J. Non-equilibrium. Thermodyne. 49 (2024), 1–21]. We study the non-equilibrium irreversible thermodynamics (NIT) properties of the exact solution to the dilute non-homogeneously charged gas problem with unsteady Rayleigh flow. In contrast to previous research, the charged gas is non-homogeneous under the influence of induced electromagnetic forces, the flat plate moving damping with time, and the effect of positive ions is considered, leading to significant advancements in understanding natural plasma dynamics. We are solving eight non-homogeneous partial differential equations (PDE). We used a Laplace transformation technique and small parameters methods. To the best of our knowledge, as two new scientific achievements, we introduced a new mathematical model for a mixture of charged gas to calculate the thermodynamic forces, kinetic coefficients, and fluxes variables, see Appendices. Second, we present a fantastic new technique by a flowchart to identify the equilibrium time of multi-component plasma step-by-step using the velocity distribution function (VDF). We indicate that electrons, which are faster lighter components, reach equilibrium faster than slower heavier components. A standard laboratory argon plasma model is used to apply the results. [ABSTRACT FROM AUTHOR]

The stability of homogeneous thermodynamic equilibrium is analyzed in heat conduction theories in the framework of nonequilibrium thermodynamics, where the internal energy, the heat flux and a second order tensor are thermodynamic state variables. It is shown, that the thermodynamic conditions of concave entropy and nonnegative entropy production can ensure the linear stability. Various special heat conduction theories, including Extended Thermodynamics, are compared in the general framework. [ABSTRACT FROM AUTHOR]

Mass and thermodiffusion are transport phenomena in fluid mixtures important in many applications. In this paper it is argued that these transport phenomena have even become more interesting in view of some surprising discoveries from fluctuating hydrodynamics leading to possible new emerging issues in non-equilibrium thermodynamics. A short review of the history of this subject is presented. The paper then addresses the problem that the conventional mass and thermodiffusion coefficients depend on the frame of reference. A simple solution to this problem is elucidated. [ABSTRACT FROM AUTHOR]

In this work, we present a review of Energy-Momentum Squared Gravity (EMSG)—more specifically, f (R , T μ ν T μ ν) gravity, where R represents the Ricci scalar and T μ ν denotes the energy-momentum tensor. The inclusion of quadratic contributions from the energy-momentum components has intriguing cosmological implications, particularly during the Universe's early epochs. These effects dominate under high-energy conditions, enabling EMSG to potentially address unresolved issues in General Relativity (GR), such as the initial singularity and aspects of big-bang nucleosynthesis in certain models. The theory's explicit non-minimal coupling between matter and geometry leads to the non-conservation of the energy-momentum tensor, which prompts the investigation of cosmological scenarios through the framework of irreversible thermodynamics of open systems. By employing this formalism, we interpret the energy-balance equations within EMSG from a thermodynamic perspective, viewing them as descriptions of irreversible matter creation processes. Since EMSG converges to GR in a vacuum and differences emerge only in the presence of an energy-momentum distribution, these distinctions become significant in high-curvature regions. Therefore, deviations from GR are expected to be pronounced in the dense cores of compact objects. This review delves into these facets of EMSG, highlighting its potential to shed light on some of the fundamental questions in modern cosmology and gravitational theory. [ABSTRACT FROM AUTHOR]

This paper provides a perspective on applying the concepts of information thermodynamics, developed recently in non-equilibrium statistical physics, to problems in theoretical neuroscience. Historically, information and energy in neuroscience have been treated separately, in contrast to physics approaches, where the relationship of entropy production with heat is a central idea. It is argued here that also in neural systems, information and energy can be considered within the same theoretical framework. Starting from basic ideas of thermodynamics and information theory on a classic Brownian particle, it is shown how noisy neural networks can infer its probabilistic motion. The decoding of the particle motion by neurons is performed with some accuracy, and it has some energy cost, and both can be determined using information thermodynamics. In a similar fashion, we also discuss how neural networks in the brain can learn the particle velocity and maintain that information in the weights of plastic synapses from a physical point of view. Generally, it is shown how the framework of stochastic and information thermodynamics can be used practically to study neural inference, learning, and information storing. [ABSTRACT FROM AUTHOR]

So-called strength-ductility trade-off is usually an inevitable scenario in precipitation-strengthened alloys. To address this challenge, high-density coherent nanoprecipitates (CNPs) as a microstructure effectively promote ductility though multiple interactions between CNPs and dislocations (i.e., coherency, order, or Orowan mechanism). Although some strain hardening theories have been reported for individual strengthening, how to increase, artificially and quantitatively, the ductility arising from cooperative strengthening due to the multiple interactions has not been realized. Accordingly, a dislocation-based theoretical framework for strain hardening is constructed in terms of irreversible thermodynamics, where nucleation, gliding, and annihilation arising from dislocations have been integrated, so that the cooperative strengthening can be treated through thermodynamic driving force ∆ G and the kinetic energy barrier. Further combined with synchrotron high-energy X-ray diffraction, the current model is verified. Following the modeling, the yield stress σ y is proved to be correlated with the modified strengthening mechanism, whereas the necking strain ε n is shown to depend on the evolving dislocation density and, essentially, the enhanced activation volume. A criterion of high ∆ G -high generalized stability is proposed to guarantee the volume fraction of CNPs improving σ y and the radius of CNPs accelerating ε n . This strategy of breaking the strength-ductility trade-off phenomena by controlling the cooperative strengthening can be generalized to designing metallic structured materials. [ABSTRACT FROM AUTHOR]

In the literature, one can find numerous modifications of Fourier's law, the first of which is the Maxwell–Cattaneo–Vernotte heat equation. Although this model has been known for decades and successfully used to model low-temperature damped heat wave propagation, its nonlinear properties are rarely investigated. This paper aims to present the functional relationship between the transport coefficients and the consequences of their temperature dependence, particularly focusing on thermal conductivity. These are the consequences of the second law of thermodynamics. Furthermore, we introduce a particular implicit numerical scheme in order to solve such nonlinear heat equations reliably, free from artificial numerical errors. We investigate the scheme's stability, dissipation, and dispersion attributes. We demonstrate the effect of temperature-dependent thermal conductivity on two different initial-boundary value problems, including time-dependent boundaries and heterogeneous initial conditions, for which we discuss the nontrivial constraints following irreversible thermodynamics. [ABSTRACT FROM AUTHOR]

Salt weathering is a common deterioration phenomenon that affects outdoor cultural properties, and it is important to precisely predict the heat, moisture, and salt transfer in porous materials to suppress salt weathering. Osmosis and osmotic pressure were considered in the field of soil research, especially in clay research, but not in the field of outdoor cultural properties and building materials, which are the main target of salt weathering. Osmosis in clay is supposed to be caused by its surface charge. However, it has been suggested that sandstones and bricks that constitute cultural properties and buildings also have surface charge as clay. Thus, osmosis and osmotic pressure can occur in building materials, which may lead to materials degradation. In this study, we derive basic equations, based on nonequilibrium thermodynamics, for the simultaneous heat, dry air, water vapor, liquid water, cation, and anion transfer in building materials by considering osmosis. This equation was compared with existing model for heat and moisture transfer equations as well as models that considered the salt transfer. Based on the previous research for osmosis in clay, we summarized conditions under which osmosis occurs in building materials and presented an outlook for modeling the physical properties of materials related to osmosis. [ABSTRACT FROM AUTHOR]

In this article, we analyse the fractional Cattaneo heat equation for studying the conduction of heat in porous medium. This equation is also used in studying extended irreversible thermodynamics, material, plasma, cosmological model, computational biology, and diffusion theory in crystalline solids. The Sumudu adomian decomposition technique, which is combination of Sumudu transform and a numerical technique, is applied for getting numerical solution. The existence and uniqueness is analysed by using the fixed point theorem and the highest error of the designed technique is also analysed. Finally, the accuracy of the designed numerical method is presented by solving two examples and the findings are compared with the existing method. [ABSTRACT FROM AUTHOR]

Quantum thermodynamics aims to extend standard thermodynamics and nonequilibrium statistical physics to systems with sizes well below the thermodynamic limit. It is a rapidly evolving research field that promises to change our understanding of the foundations of physics, while enabling the discovery of novel thermodynamic techniques and applications at the nanoscale. Thermal management has turned into a major obstacle in pushing the limits of conventional digital computers and could also represent a crucial issue for quantum computers. The practical realization of quantum computers with superconducting loops requires working at cryogenic temperatures to eliminate thermal noise, and ion-trap qubits also need low temperatures to minimize collisional noise. In both cases, the sub-nanometric sizes also bring about the thermal broadening of the quantum states; and even roomtemperature photonic computers eventually require cryogenic detectors. A number of thermal and thermodynamic questions, therefore, take center stage, such as quantum re-definitions of work and heat, thermalization and randomization of quantum states, the overlap of quantum and thermal fluctuations, and many others, even including a proper definition of temperature for the small open systems constantly out of equilibrium that are the qubits. This overview provides an introductory perspective on a selection of current trends in quantum thermodynamics and their impact on quantum computers and quantum computing, with language that is accessible to postgraduate students and researchers from different fields. [ABSTRACT FROM AUTHOR]

The close intertwining of equilibrium and nonequilibrium thermodynamic representations and transitions between two limiting principles of thermodynamics: the second beginning and the principle of least coercion (minimum entropy production in the stationary regime) constitute the main content of the phenomenological theories of crystal growth. The difference of the basic postulates of two sections of thermodynamics forces to discuss the problems of reversibility and irreversibility of time, scales of observed phenomena, and rules of conjugation of thermodynamic forces and flows in theories of crystal growth. A variant of the solution of some conjugation problems is shown on the example of the fluctuation model of dislocation crystal growth, which is based on the stationary isothermal process of thermodynamic free energy fluctuations. In the case of the limiting mode of adsorption of impurities on the crystal face according to the Langmuir model, the free-energy fluctuations characterized by the absence of the memory effect make it possible to identify three chemical potentials of building particles, which determine the corresponding values of solution supersaturations realized at different scale levels at the growing crystal face containing a screw dislocation. The supersaturations control quasi-equilibrium and nonequilibrium thermodynamic processes that constitute a unified dislocation mechanism of crystal growth. [ABSTRACT FROM AUTHOR]

Geological sequestration is an established method to store carbon deep underground. Many studies have proposed coupled constitutive models that can simulate such a complicated process; however, the coupling effect of multi-phase fluid flow and transport of chemical solutes in the liquid phase remains to be investigated. This study presents a multi-phase non-reactive hydro-mechanical-chemical constitutive framework under isothermal conditions based on mixture coupling theory. Non-equilibrium thermodynamics is used to generate an entropy production equation, and phenomenological equations use this to derive the chemical transport and interaction between two-phase fluid flows. This study proposes novel terms in the final governing equations. The model results are in good agreement with the results of a benchmark experiment and those found in the literature; the model has been used to compare the behaviour of carbon dioxide in the gas and supercritical phases. Sensitivity analysis was conducted to determine the effect of the parameters in the new terms. Sensitivity analysis revealed the significant impact of relative permeability and saturation values on the new terms, emphasising the importance of understanding frictional behaviour in porous media for accurate fluid flow modelling and prediction. This study urges further experimentation and model refinement to improve carbon sequestration modelling in larger formations. [ABSTRACT FROM AUTHOR]

Relaxation modes must be considered coupled on several occasions, such as in polymer blends. Edwards et al. [J. Rheol, 40, 917–942 (1996)], using the generalized bracket formalism of non-equilibrium thermodynamics, provided the first thermodynamically derived constitutive model with coupled Maxwell modes by introducing relaxation coupling between the modes. In this work, we derive a similar model wherein coupling is introduced by using Giesekus' postulate to the mobility tensor and its introduction in the relaxation matrices, without considering cross-relaxation matrices. Our approach bears the following advantages over the work of Edwards et al.: (a) it derives the coupling term, instead of simply invoking it, by using the Giesekus postulate, (b) it is more in line with rheological experimental data for polymer blends, and (c) the proof of thermodynamic admissibility is easier to perform. [ABSTRACT FROM AUTHOR]

We consider three different systems in a heat flow: an ideal gas, a van der Waals gas, and a binary mixture of ideal gases. We divide each system internally into two subsystems by a movable wall. We show that the direction of the motion of the wall, after release, under constant boundary conditions, is determined by the same inequality as in equilibrium thermodynamics d U − đ Q ≤ 0 . The only difference between the equilibrium and non-equilibrium laws is the dependence of the net heat change, đ Q , on the state parameters of the system. We show that the same inequality is valid when introducing the gravitational field in the case of both the ideal gas and the van der Waals gas in the heat flow. It remains true when we consider a thick wall permeable to gas particles and derive Archimedes' principle in the heat flow. Finally, we consider the Couette (shear) flow of the ideal gas. In this system, the direction of the motion of the internal wall follows from the inequality d E − đ Q − đ W s ≤ 0 , where d E is the infinitesimal change in total energy (internal plus kinetic) and đ W s is the infinitesimal work exchanged with the environment due to the shear force imposed on the flowing gas. Ultimately, we synthesize all these cases within a general framework of the second law of non-equilibrium thermodynamics. [ABSTRACT FROM AUTHOR]

Migration of colloidal particles induced by temperature gradients is commonly referred to as thermodiffusion, thermal diffusion, or the (Ludwig-)Soret effect. The thermophoretic force experienced by a colloidal particle that drives thermodiffusion consists of two distinct contributions: a contribution resulting from internal degrees of freedom of single colloidal particles, and a contribution due to the interactions between the colloids. We present an irreversible thermodynamics based theory for the latter collective contribution to the thermophoretic force. The present theory leads to a novel "thermophoretic interaction force" (for uncharged colloids), which has not been identified in earlier approaches. In addition, an N -particle Smoluchowski equation including temperature gradients is proposed, which complies with the irreversible thermodynamics approach. A comparison with experiments on colloids with a temperature dependent attractive interaction potential over a large concentration and temperature range is presented. The comparison shows that the novel thermophoretic interaction force is essential to describe data on the Soret coefficient and the thermodiffusion coefficient. • An irreversible thermodynamics based theory is presented leading to a novel "thermophoretic interaction force" on colloidal particles that originates from their mutual interactions. • Explicit microscopic expressions are found for the Soret coefficient and the thermodiffusion coefficient in terms of the (equilibrium) pair-correlation function. • The novel thermophoretic interaction force is essential to be able to describe the experimental data. [ABSTRACT FROM AUTHOR]

In this work, we derive a homogenized mathematical model for a porous intercalation electrode with a phase separating active material. We start from a microscopic model consisting of transport equations for lithium ions in an electrolyte phase and intercalated lithium in a solid active phase. Both are coupled through a Neumann–boundary condition modeling the lithium intercalation reaction Li+ + e- ⇌ Li. . The active material phase is considered to be phase separating upon lithium intercalation. We assume that the porous material is a given periodic microstructure and perform analytical homogenization. Effectively, the microscopic model consists of a diffusion and a Cahn–Hilliard equation, whereas the limit model consists of a diffusion and an Allen–Cahn equation. Thus, we observe a Cahn–Hilliard to Allen–Cahn transition during the upscaling process. In the sense of gradient flows, the transition coincides with a change in the underlying metric structure of the PDE system. [ABSTRACT FROM AUTHOR]

Temperature serves as a critical yet elusive factor impacting the mechanical properties of deep rocks. In this work, we shall develop a new micro‐thermomechanical model for rocks based on the Mori‐Tanaka homogenization scheme. Free energy and thermodynamic forces are deduced within the framework of irreversible thermodynamics, including the local stress applied on the mesocracks, damage driving force, macroscopic stress, and entropy. The salient innovation of this study lies in formulating subtle physically based temperature‐dependent friction and damage laws, considering the influence of ambient temperature on the mesocracking in rocks. Through a coupled friction‐damage analysis, a temperature‐dependent quasi‐static strength criterion and analytical stress‐strain‐damage relations are then derived. Physical implications and calibration methods of each parameter in the proposed model are meticulously presented. Furthermore, a semi‐implicit plasticity damage decoupled procedure (SIPDDC) integration algorithm is employed for the numerical implementation of the proposed model. Subsequently, numerical simulations are conducted to obtain the mechanical response of Jinping marble, Beibei sandstone, and Gongjue granite under various real‐time temperature‐confining pressure coupling conventional triaxial compression tests (TP‐CTC). The congruence of stress‐strain curves between model predictions and experimental data validates the robust performance and potential applicability of the proposed model. Plain Language Summary: High ground temperatures have a crucial influence on the stability of deep rocks. Establishing a robust calculation model is paramount for the feasibility and reliability analysis of deep rock engineering. However, incorporating mesocracking mechanisms into such models remains challenging. This paper presents an advanced micro‐thermomechanical model based on homogenization theory, aiming to investigate the macro‐ and micromechanical behaviors of rocks under different ambient temperature conditions. The model innovatively considers the temperature‐dependent characteristics of mesocracking. The model demonstrates satisfactory numerical performance and can effectively capture temperature‐dependent mechanical behaviors of three typical rocks, that is, marble, sandstone, and granite. This work provides a new perspective from a micromechanical standpoint for the theoretical and engineering analysis of deep rock mechanics under high‐temperature and high‐pressure conditions. Key Points: A homogenization‐based micro‐thermomechanical constitutive model is established considering temperature‐dependent friction and damage lawsA temperature‐dependent strength criterion and analytical damage‐stress‐strain relations are derived through cross‐scaling analysisThe model possesses robust numerical performance and shows a promising application prospect in deep rock engineering analysis [ABSTRACT FROM AUTHOR]

In this paper, we explore into the stochastic thermodynamics of a finite-tape information ratchet system. By determining the entropy production of the tape-ratchet system, we derive the information processing second law obeyed by the system. We found that the entropy production takes the form of the non-adiabatic component in both the transient and stationary regime, with the adiabatic component vanishes. The out-of-equilibrium stochastic behaviour is thus driven by non-adiabatic entropy production, with the occurrence of spontaneous relaxation from nonequilibrium initial state and the switching operation of the finite-tape information ratchet system. The observed nonequilibrium processes include (1) work extraction by assimilating excess heat from the heat reservoir when the information ratchet functions as an engine, or (2) dissipating work as excess heat into the heat reservoir when the information ratchet acts as a Landauer eraser. In particular, we observe the phenomenon of irreversible work conversion into excess heat as the information ratchet operates in the nonequilibrium stationary state. [ABSTRACT FROM AUTHOR]

The complete description of energy and material transport within the Generalized energy-conserving dissipative particle dynamics with mass transfer (GenDPDE-M) methodology is presented. In particular, the dynamic coupling between mass and energy is incorporated into the GenDPDE-M, which was previously introduced with dynamically decoupled fluxes (J. Bonet Avalos et al., J. Chem. Theory Comput., 18 (12): 7639–7652, 2022). From a theoretical perspective, we have derived the appropriate Fluctuation-Dissipation theorems along with Onsager's reciprocal relations, suitable for mesoscale models featuring this coupling. Equilibrium and non-equilibrium simulations are performed to demonstrate the internal thermodynamic consistency of the method, as well as the ability to capture the Ludwig–Soret effect, and tune its strength through the mesoscopic parameters. In view of the completeness of the presented approach, GenDPDE-M is the most general Lagrangian method to deal with complex fluids and systems at the mesoscale, where thermal agitation is relevant. [ABSTRACT FROM AUTHOR]

The balance equation of angular momentum in anisotropic fluids includes a couple stress contribution, also responsible for an antisymmetric contribution to the force stress tensor. We herein derive all balance equations for the simplest anisotropic fluid, i.e., a polar fluid, using the GENERIC formalism of non-equilibrium thermodynamics. In doing so, we find that there is an inconsistency between the internal energy density evolution equation derived using non-equilibrium thermodynamics and the one usually considered in micropolar theory. [ABSTRACT FROM AUTHOR]

In this paper, we present a comprehensive account of quantum dissipation theories with the quadratic environment couplings. The theoretical development includes the Brownian solvation mode embedded hierarchical quantum master equations, a core-system hierarchy construction that verifies the extended dissipaton equation of motion (DEOM) formalism [R. X. Xu et al., J. Chem. Phys. 148, 114103 (2018)]. Developed are also the quadratic imaginary-time DEOM for equilibrium and the λ(t)-DEOM for nonequilibrium thermodynamics problems. Both the celebrated Jarzynski equality and Crooks relation are accurately reproduced, which, in turn, confirms the rigorousness of the extended DEOM theories. While the extended DEOM is more numerically efficient, the core-system hierarchy quantum master equation is favorable for "visualizing" the correlated solvation dynamics. [ABSTRACT FROM AUTHOR]

Thermogalvanic cells convert waste heat directly to electric work. There is an abundance of waste heat in the world and thermogalvanic cells may be underused. We discuss theoretical tools that can help us understand and therefore improve on cell performance. One theory is able to describe all aspects of the energy conversion: nonequilibrium thermodynamics. We recommend to use the theory with operationally defined, independent variables, as others have done before. These describe well-defined experiments. Three invariance criteria serve as a basis for any description: of local electroneutrality, entropy production invariance, and emf's independence of the frame of reference. Alternative formalisms, using different sets of variables, start with ionic or neutral components. We show that the heat flux is not the same in the two formalisms and derive a new relationship between the heat fluxes. The heat flux enters the definition of the Peltier coefficient and is essential for the understanding of the Peltier heat at the electrode interfaces and of the Seebeck coefficient of the cell. The Soret effect can occur independently of any Seebeck effect, but the Seebeck effect will be affected by the presence of a Soret effect. Common misunderstandings are pointed out. Peltier coefficients are needed for the interpretation and design of experiments. [ABSTRACT FROM AUTHOR]

There is a long-standing question as to whether and to what extent it is possible to describe nonequilibrium systems in stationary states in terms of global thermodynamic functions. The positive answers have been obtained only for isothermal systems or systems with small temperature differences. We formulate thermodynamics of the stationary states of the ideal gas subjected to heat flow in the form of the zeroth, first, and second law. Surprisingly, the formal structure of steady state thermodynamics is the same as in equilibrium thermodynamics. We rigorously show that U satisfies the following equation dU = T*dS* − pdV for a constant number of particles, irrespective of the shape of the container, boundary conditions, the size of the system, or the mode of heat transfer into the system. We calculate S* and T* explicitly. The theory selects stable nonequilibrium steady states in a multistable system of ideal gas subjected to volumetric heating. It reduces to equilibrium thermodynamics when heat flux goes to zero. [ABSTRACT FROM AUTHOR]

After more than a century of concerted effort, physics still lacks basic principles of spontaneous self-organization. To appreciate why, we first state the problem, outline historical approaches, and survey the present state of the physics of self-organization. This frames the particular challenges arising from mathematical intractability and the resulting need for computational approaches, as well as those arising from a chronic failure to define structure. Then, an overview of two modern mathematical formulations of organization—intrinsic computation and evolution operators—lays out a way to overcome these challenges. Additionally, we show how intrinsic computation and evolution operators combine to produce a general framework showing physical consistency between emergent behaviors and their underlying physics. This statistical mechanics of emergence provides a theoretical foundation for data-driven approaches to organization necessitated by analytic intractability. Taken all together, the result is a constructive path towards principles of organization that builds on the mathematical identification of structure. [ABSTRACT FROM AUTHOR]

The general relativity unification and quantum theory is a significant open problem in theoretical physics. This problem arises from the fact that these two fundamental theories, which describe gravity and the behavior of particles at the microscopic level, respectively, are currently incompatible. The unification of these theories is crucial for a complete comprehension of the fundamental forces and the nature of the universe. In this regard, the quantum properties of a Black Hole result in fundamental importance. By analyzing such properties in quantum field theory, in the first step, the gravity enters as a classical background. In semi-classical approximation, Black Holes will emit Hawking radiation with an almost thermal spectrum, while Black Hole's entropy is proportional to the Black Hole's horizon. Besides, Hawking's temperature and Black Hole entropy should follow the first law of Black Hole thermodynamics. Also, Jacobson [Thermodynamics of spacetime: The Einstein equation of state, Phys. Rev. Lett.75 (1995) 1260, doi:10.1103/PhysRevLett.75.1260] showed shown that there is a connection between Black Hole thermodynamics and Einstein's equation that opens the root of a potential thermodynamic nature of gravity. This issue opened a new impressive research framework in which the Einstein field equation can be expressed as a form of the first law of thermodynamics and vice versa. In this study, it is assumed that the universe has a fractal structure. Accordingly, modified Friedmann's equations and the Black Holes thermodynamics in a fractal universe have been examined. The fractal framework shows what features and changes occur in the description of the universe, particularly in studying the thermodynamics of a Black Hole. However, the paper strategy is organized as follows: in the beginning, we consider the first thermodynamic law in a fractal universe. Then, we investigate the Friedmann equation of the fractal universe in the form of the entropy balance, this means d Q = T h d S h , where d Q and T h are the thermal energy and horizon temperature. We consider the entropy S h have two terms; (1) obeys the usual area law and (2) the entropy production term due to the non-equilibrium thermodynamics of a fractal universe. Therefore, in a fractal universe, a term with non-equilibrium thermodynamics of spacetime may be needed. Also, we study the generalized second law of thermodynamics in a fractal universe. When the temperature of the apparent horizon and the temperature of the matter fields inside the horizon are equal, i.e. T = T h , the second law of generalized thermodynamics can be obtained according to the state parameter range equation, which is consistent with the recent observations. Finally, in Sec. 6, based on the mathematical calculations, we study the various cosmological parameters such as the Hubble parameter, scale factor, deceleration parameter and equation of state parameter. [ABSTRACT FROM AUTHOR]

Starting from the analysis of the lack of positivity of the Cattaneo heat equation, this work addresses the thermodynamic relevance of the positivity constraint in irreversible thermodynamics, that is at least as significant as the entropic constraints. The fulfillment of this condition in hyperbolic models leads to the parametrization of the concentration fields with respect to internal variables associated with the microscopic dynamics. Using Brownian motion theory as a landmark example for deriving macroscopic transport equations from the equations of motion at the particle/molecular level, we discuss two typical problems involving hydrodynamic interactions at the microscale: surface chemical reactions at a solid interface of a diffusing reactant, and mass-balance equations in a complex viscoelastic fluid, in which the physics of the interaction leads either to overcoming the parabolic diffusion model or to considering the parametrization of the concentration with respect to the degrees of freedom associated with the relaxation dynamics of the solvent fluid. [ABSTRACT FROM AUTHOR]