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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]

Living systems operate within physical constraints imposed by nonequilibrium thermodynamics. This review explores recent advancements in applying these principles to understand the fundamental limits of biological functions. We introduce the framework of stochastic thermodynamics and its recent developments, followed by its application to various biological systems. We emphasize the interconnectedness of kinetics and energetics within this framework, focusing on how network topology, kinetics, and energetics influence functions in thermodynamically consistent models. We discuss examples in the areas of molecular machine, error correction, biological sensing, and collective behaviors. This review aims to bridge physics and biology by fostering a quantitative understanding of biological functions. [ABSTRACT FROM AUTHOR]

In this investigation, the principles of non-equilibrium thermodynamics are employed to investigate the implications of geometric parameters on engine performance and exhaust back pressure in catalytic converters. The effects of components utilized for engine exhaust management on exhaust back pressure and anomalous engine operation have been extensively studied. This study explores how the geometric parameters of catalytic converters influence back pressure in the exhaust manifold through a detailed numerical analysis. Five models of catalytic converter with different geometric parameters at the inlet section, outlet section, inlet cone angle, outlet cone angle, and porous zone were tested to determine the variations in back pressure. For the monolith, a porous region is used where inertia and viscosity are defined by Darcy’s law, and discrete channel simulation is performed using the “Reynolds-average Naiver-Stokes (RANS) equations”, k-ω turbulence model, and a pressure-based solver. The numerical findings revealed that back pressure increased by up to 15 % with the rise in exhaust gas velocity from 0 to 25 m/s. Among the five models, the optimal configuration reduced back pressure by approximately 20 % compared to the baseline model, primarily due to adjustments in the length of the porous zone and conical sections. The outcomes demonstrate that the back pressure rises as the velocity of exhaust gas rises, and the optimization of configurations is determined by the design of the porous zone and conical sections. The findings prove that the efficiency of catalytic converters is considerably enhanced through the role of transport processes of mass, momentum, and energy, as variations in geometric configurations have a substantial effect on back pressure. Ultimately, this research offers valuable insights that could lead to the development of more efficient catalytic converters, thereby enhancing the control of automotive emissions and sustainable environmental practices. Key contributions of this study include a systematic evaluation of back pressure variations across multiple geometries, offering a pathway for enhanced engine performance and reduced environmental impact. The results have practical implications in improving design methodologies for catalytic converters, with potential applications in real-world automotive manufacturing. [ABSTRACT FROM AUTHOR]

Phase diagrams out of equilibrium have been the subject of intense research. An essential concept in these diagrams is the phase definition. Currently, that definition is well established for systems at classic thermodynamic equilibrium conditions. However, such phase definition is inadequate for systems that are not at equilibrium in the classic thermodynamic sense, like fluid systems under flowing conditions. Complex fluids may exhibit instabilities like shear-banding flow and a non-equilibrium critical point where banding flow ends. At this point, the fluid undergoes a phase transition from heterogeneous to homogeneous states. An extended thermodynamic space of variables is considered to adequately address this situation, which includes non-conservative variables such as stress and shear rate. Hence, the current phase definition based on conservative variables does not apply to non-equilibrium phase diagrams. On this basis, a broader definition of phase is required. We propose that this broader definition considers the thermodynamic variables space of Extended Irreversible Thermodynamics and the mathematical conditions that ensure compatibility between equilibrium and non-equilibrium conditions for systems where phases are well described by thermodynamic potentials even out of equilibrium. [ABSTRACT FROM AUTHOR]

The exploration of far-from-equilibrium systems has been at the forefront of nonequilibrium thermodynamics, with a particular focus on understanding the fluctuations and response of thermodynamic systems to external perturbations. In this study, we introduce a universal response kinetic uncertainty relation, which provides a fundamental trade-off between the precision of response for generic observables and dynamical activity in Markovian nonequilibrium systems. We demonstrate the practical applicability and tightness of the derived bound through illustrative examples. Our results are applicable to a broad spectrum of Markov jump processes, ranging from currents to non-current variables, from steady states to time-dependent driving, from continuous time to discrete time, and including Maxwell's demon or absolute irreversibility. Our findings not only enhance the theoretical foundation of stochastic thermodynamics but also may hold potential implications for far-from-equilibrium biochemical processes. The thermodynamics and kinetics of a nonequilibrium classical system fundamentally constrain the precision of an observable according to the thermodynamic and kinetic uncertainty relations. This study introduces a fundamental trade-off between the precision of response for various observables and the dynamical activity in far-from-equilibrium systems, with significant implications for stochastic thermodynamics and biochemical processes. [ABSTRACT FROM AUTHOR]

Unfortunately, the scientific research concerned with the micro-scale mathematical models in plasma has very few numbers compared with the other mathematical models. However, the microscopic fields are related to all modern technology like nano and micro technology, quantum computers, and many other essential applications. This study focuses on the mathematical analysis of a micro-scale Boltzmann-Maxwell partial differential equations (PDE) system for a gaseous plasma flow influenced by a non-linear, non-uniform external electric field, specifically in the context of a novel irreversibility micro-scale analysis of the kinetic theory of plasma. We did that using the analytical solution of the PDE system. The governing equations were developed using the moment and traveling-wave techniques in a new irreversible non-equilibrium thermodynamics (INT) methodology. To our knowledge, this was applied for the first time. We are investigating the distinct behavior of the electron velocity distribution functions (VDF) and the non-equilibrium velocity functions, representing an essential INT novel study. As a result, critical micro-scale INT variables would employ the generated non-equilibrium VDF to get the equilibrium time for each species. We aim to show how the impacts of various thermodynamic forces on internal energy change (IEC) are maintained. The research generates visual representations of physical variables in 3D. Extensive physics, electric manufacturing, and nano-electro-mechanical systems applications in various manufacturing contexts attest to the research's standing. We aim to calculate the percentages between the numerous contributions of IEC in diamagnetic and paramagnetic plasma based on the total derivatives of the extensive parameters. We apply the results to a typical model of laboratory helium plasma because of the helium's various excellent applications. • The most significant values of the three IEA effects in the diamagnetic scenario are given in the following order of amplitude: dU S (10 , 10) : dU pol (10 , 10) : dU dia 10 , 10 = 1 : − 0.1 × 10 6 : 0.1 × 10 − 1. • We have developed a novel mathematical approach for estimating thermodynamic forces, kinetic coefficients, and kinetic fluxes variables. • Our mathematical model aligns with non-equilibrium thermodynamic concepts, including Gibbs's formula, Le Chatelier's principle, Boltzmann's H-theorem. • The study reveals that the electric field's wave shape significantly impacts plasma systems. • Over time, we found that entropy is the primary factor responsible for the most substantial alteration in internal energy. [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]

Dissipation and irreversibility are two central concepts of classical thermodynamics that are often treated as synonymous. Dissipation D is lost or dissipated work W diss ≥ 0 but is commonly quantified by entropy generation Δ i S in an isothermal irreversible macroscopic process that is often expressed as Kullback–Leibler distance D KL in modern literature. We argue that D KL is nonthermodynamic, and is erroneously justified for quantification by mistakenly equating exchange microwork Δ e W k with the system-intrinsic microwork Δ W k = Δ e W k + Δ i W k , which is a very common error permeating stochastic thermodynamics as was first pointed out several years ago, see text. Recently, it is discovered that dissipation D is properly identified by Δ i W ≥ 0 for all spontaneously irreversible processes and all temperatures T, positive and negative in an isolated system. As T plays an important role in the quantification, dissipation allows for Δ i S ≥ 0 for T > 0 , and Δ i S < 0 for T < 0 , a surprising result. The connection of D with W diss and its extension to interacting systems have not been explored and is attempted here. It is found that D is not always proportional to Δ i S . The determination of D requires d i p k , but we show that Fokker-Planck and master equations are not general enough to determine it, which is contrary to the common belief. We modify the Fokker-Planck equation to fix the issue. We find that detailed balance also allows for all microstates to remain disconnected without any transition among them in an equilibrium macrostate, another surprising result. We argue that Liouville's theorem should not apply to irreversible processes, contrary to the claim otherwise. We suggest to use nonequilibrium statistical mechanics in extended space, where p k 's are uniquely determined to evaluate D. [ABSTRACT FROM AUTHOR]

Peusner's network thermodynamics (PNT) is an important way of describing processes in nonequilibrium thermodynamics. PNT allows energy transport and conversion processes in membrane systems to be described. This conversion concerns internal energy transformation into free and dissipated energies linked with the membrane transport of solutes. A transformation of the Kedem–Katchalsky (K-K) equations into the R variant of Kedem–Katchalsky–Peusner (K-K-P) equations was developed for the transport of binary electrolytic solutions through a membrane. The procedure was verified for a system in which a membrane Ultra Flo 145 Dialyser separated aqueous NaCl solutions. Peusner coefficients were calculated by the transformation of the K-K coefficients. Next, the coupling coefficients of the membrane processes and energy fluxes for electrolyte solutions transported through the membrane were calculated based on the Peusner coefficients. The efficiency of energy conversion in the membrane transport processes was estimated, and this coefficient increased nonlinearly with the increase in the solute concentration in the membrane. In addition, the energy fluxes as functions of ionic current density for constant solute fluxes were also investigated for membrane transport processes in the Ultra Flo 145 Dialyser membrane. [ABSTRACT FROM AUTHOR]

Entropy production is a key descriptor of out-of-equilibrium behavior in active matter systems, providing insights into both single-particle dynamics and emergent collective phenomena. It helps determine transport coefficients and phoretic velocities and serves as a crucial tool for understanding collective phenomena such as structural transitions, regime shifts, clustering, and self-organization. This study investigates the role of entropy production for individual active (catalytic Janus) particles and in systems of active particles interacting with one another and their environment. We employ a multiscale framework to bridge microscopic particle dynamics and macroscopic behavior, offering a thermodynamic perspective on active matter. These findings enhance our understanding of the fundamental principles governing active particle systems and create new opportunities for addressing unresolved questions in non-equilibrium thermodynamics. [ABSTRACT FROM AUTHOR]

Extended irreversible thermodynamics (EIT) has been widely used to overcome the deficiencies of classical irreversible thermodynamics in describing fast transport phenomena. By employing fluxes as additional independent variables and rejecting local equilibrium hypothesis, EIT may provide a thermodynamically consistent framework for high-frequency and non-local processes. Here, we propose an alternative approach to EIT that shares the same objective but does not reject local equilibrium hypothesis. Using the rates of change of the energy density as the additional independent variable, we illustrate this approach for two typical problems of transient heat conduction: the Cattaneo-type flux model with thermodynamic inertia and the two-temperature model of energy transfer in a phonon–electron system. [ABSTRACT FROM AUTHOR]

We develop finite element methods for coupling the steady-state Onsager–Stefan–Maxwell (OSM) equations to compressible Stokes flow. These equations describe multicomponent flow at low Reynolds number, where a mixture of different chemical species within a common thermodynamic phase is transported by convection and molecular diffusion. Developing a variational formulation for discretizing these equations is challenging: the formulation must balance physical relevance of the variables and boundary data, regularity assumptions, tractability of the analysis, enforcement of thermodynamic constraints, ease of discretization and extensibility to the transient, anisothermal and nonideal settings. To resolve these competing goals, we employ two augmentations: the first enforces the definition of mass-average velocity in the OSM equations, while its dual modifies the Stokes momentum equation to enforce symmetry. Remarkably, with these augmentations we achieve a Picard linearization of symmetric saddle point type, despite the equations not possessing a Lagrangian structure. Exploiting structure mandated by linear irreversible thermodynamics, we prove the inf-sup condition for this linearization, and identify finite element function spaces that automatically inherit well-posedness. We verify our error estimates with a numerical example, and illustrate the application of the method to nonideal fluids with a simulation of the microfluidic mixing of hydrocarbons. [ABSTRACT FROM AUTHOR]

Maximizing the amount of work harvested from an environment is important for a wide variety of biological and technological processes, from energy-harvesting processes such as photosynthesis to energy storage systems such as fuels and batteries. Here, we consider the maximization of free energy—and by extension, the maximum extractable work—that can be gained by a classical or quantum system that undergoes driving by its environment. We consider how the free energy gain depends on the initial state of the system while also accounting for the cost of preparing the system. We provide simple necessary and sufficient conditions for increasing the gain of free energy by varying the initial state. We also derive simple formulae that relate the free energy gained using the optimal initial state rather than another suboptimal initial state. Finally, we demonstrate that the problem of finding the optimal initial state may have two distinct regimes, one easy and one difficult, depending on the temperatures used for preparation and work extraction. We illustrate our results on a simple model of an information engine. [ABSTRACT FROM AUTHOR]

Vopson and Lepadatu recently proposed the Second Law of Infodynamics. The law states that while the total entropy increases, information entropy declines over time. They state that the law has applications over a wide range of disciplines, but they leave many key questions unanswered. This article analyzes and reformulates the law based on thermocontextual interpretation (TCI). The TCI generalizes Hamiltonian mechanics by defining states and transitions thermocontextually with respect to an ambient-temperature reference state. The TCI partitions energy into exergy, which can do work on the ambient surroundings, and entropic energy with zero work potential. The TCI is further generalized here to account for a reference observer's actual knowledge. This enables partitioning exergy into accessible exergy, which is known and accessible for use, and configurational energy, which is knowable but unknown and inaccessible. The TCI is firmly based on empirically validated postulates. The Second Law of thermodynamics and its information-based analog, MaxEnt, are logically derived corollaries. Another corollary is a reformulated Second Law of Infodynamics. It states that an external agent seeks to increase its access to exergy by narrowing its information gap with a potential exergy source. The principle is key to the origin of self-replicating chemicals and life. [ABSTRACT FROM AUTHOR]

The entropy production in the polarization phenomena occurring in the underlimiting regime, when an electric current circulates through a single cation-exchange membrane system, has been investigated in the 3–40 °C temperature range. From the analysis of the current–voltage curves and considering the electro-membrane system as a unidimensional heterogeneous system, the total entropy generation in the system has been estimated from the contribution of each part of the system. Classical polarization theory and the irreversible thermodynamics approach have been used to determine the total electric potential drop and the entropy generation, respectively, associated with the different transport mechanisms in each part of the system. The results show that part of the electric power input is dissipated as heat due to both electric migration and diffusion ion transports, while another part is converted into chemical energy stored in the saline concentration gradient. Considering the electro-membrane process as an energy conversion process, an efficiency has been defined as the ratio between stored power and electric power input. This efficiency increases as both applied electric current and temperature increase. [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]

The formal description of chemical reactions far from equilibrium is an open task. Chemical reactions are central to various phenomena in life, industry, and the environment. In this work, we use a variational principle within the framework of extended irreversible thermodynamics to obtain relaxation equations for the fast variables and close the balance equations. Our approach extends traditional local equilibrium thermodynamics by incorporating formal expressions for the unknown generalized equations of state, which we can expand in low and higher-order terms, allowing for a more comprehensive representation of non-linear and dissipative phenomena and capturing wave-like behaviours relevant to oscillatory chemical systems. The formalism aligns well with previous theoretical works and provides additional insights into the influence of diffusion fluxes on reaction rates. The resulting equations may describe velocity reactions with different relaxation times and diffusion reactions. We present a comparison of our results with experiments in the context of a particular chemical kinetics case. We emphasize the need for practical applications in areas like environmentally friendly chemical reaction systems. [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]

The study of biological systems by methods of physical kinetics and non-equilibrium thermodynamics often faces the difficulty of studying nonlinear processes due to the significant deviation from equilibrium. In this paper, the new variation approach is proposed that allows us to generalize the patterns of chemical processes taking into account the influence of non-equilibrium effects.The study of interrelated chemical reactions is considered as one of the applications of this theory. The new method has been developed for the general description of the kinetics of several reactions, taking into account their mutual influence on each other. Practical examples and model calculations for several reactions with varying the degrees of influence on each other are considered. The calculations performed for the several reactions allowed us to evaluate their mutual influence on the change in the reaction rate, as well as on the change in the reaction reagents concentration over time. The results obtained can be used to describe complex chemical reactions in various systems. [ABSTRACT FROM AUTHOR]

In many complex systems encountered in the natural and social sciences, mechanisms governing system dynamics at a microscale depend upon the values of state variables characterizing the system at coarse-grained, macroscale (Goldenfeld and Woese, 2011, Noble et al., 2019, and Chater and Loewenstein, 2023). State variables, in turn, are averages over relevant probability distributions of the microscale variables. Neither inferential Top-Down nor mechanistic Bottom-Up modeling alone can predict responses of such scale-entwined systems to perturbations. We describe and explore the properties of a dynamic theory that combines Top-Down information-theoretic inference with Bottom-Up, state-variable-dependent mechanisms. The theory predicts the functional form of nonstationary probability distributions over microvariables and relates the trajectories of time-evolving macrovariables to the form of those distributions. Analytic expressions for the time evolution of Lagrange multipliers from Maxent solutions allow for rapid calculation of the time trajectories of state variables even in high dimensional systems. Examples of possible applications to scale-entwined systems in nonequilibrium chemical thermodynamics, epidemiology, economics, and ecology exemplify the potential multidisciplinary scope of the theory. A worked-out low-dimension example illustrates the structure of the theory and demonstrates how scale entwinement can result in slowed recovery from perturbations, reddened time series spectra in response to white-noise input, and hysteresis upon parameter displacement and subsequent restoration. [ABSTRACT FROM AUTHOR]

The reduced density matrix that characterises the state of an open quantum system is a projection from the full density matrix of the quantum system and its environment, and there are many full density matrices consistent with a given reduced version. Without a specification of relevant details of the environment, the time evolution of a reduced density matrix is therefore typically unpredictable, even if the dynamics of the full density matrix are deterministic. With this in mind, we investigate a two-level open quantum system using a framework of quantum state diffusion. We consider the pseudorandom evolution of its reduced density matrix when subjected to an environment-driven process that performs a continuous quantum measurement of a system observable, invoking dynamics that asymptotically send the system to one of the relevant eigenstates. The unpredictability is characterised by a stochastic entropy production, the average of which corresponds to an increase in the subjective uncertainty of the quantum state adopted by the system and environment, given the underspecified dynamics. This differs from a change in von Neumann entropy, and can continue indefinitely as the system is guided towards an eigenstate. As one would expect, the simultaneous measurement of two non-commuting observables within the same framework does not send the system to an eigenstate. Instead, the probability density function describing the reduced density matrix of the system becomes stationary over a continuum of pure states, a situation characterised by zero further stochastic entropy production. Transitions between such stationary states, brought about by changes in the relative strengths of the two measurement processes, give rise to finite positive mean stochastic entropy production. The framework investigated can offer useful perspectives on both the dynamics and irreversible thermodynamics of measurement in quantum systems. [ABSTRACT FROM AUTHOR]

Hillert often used the combined first and second law of thermodynamics to discuss and derive the principles of equilibrium as well as non-equilibrium thermodynamics. His method will now be reviewed and applied to reactions in homogeneous systems as well as transport processes As an example of homogeneous systems undercooled liquids and glasses is discussed. [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]

Thermodynamics is a theory based on phenomenological premises and has wide applicability in science and technology. However, it remains one of the most challenging subjects to understand and teach, which makes it an excellent candidate for research and development of teaching methods. In this research, a questionnaire was used to evaluate the current knowledge of Bachelor's and Master's physics students, analyzing their immediate understanding of the topic and exploring their reasoning and thought processes. The questionnaire is divided into three sections which sequentially examine high school knowledge of entropy and thermodynamics; understanding of (ir)reversible processes related to energy and entropy change; and the distinction between equilibrium and nonequilibrium states. Based on the analysis of the results, we identified difficulties in understanding and articulating and applying the learned concepts. In particular, misunderstandings of entropy changes in isothermal processes and isolated systems are observed among students at all levels. Additionally, students find it difficult to distinguish between the contributions of energy and entropy changes to a system and its environment in the processes. The difficulty in defining (non)equilibrium states is present among Bachelor's second-year physics students. To address these challenges, we propose adjustments to the teaching approach, including discussions about entropy sources and process (ir)reversibility, incorporating more theoretical and everyday examples of various processes and (non)equilibrium states and allowing more time for student discussions. [ABSTRACT FROM AUTHOR]

Self-organization in complex systems is a process associated with reduced internal entropy and the emergence of structures that may enable the system to function more effectively and robustly in its environment and in a more competitive way with other states of the system or with other systems. This phenomenon typically occurs in the presence of energy gradients, facilitating energy transfer and entropy production. As a dynamic process, self-organization is best studied using dynamic measures and principles. The principles of minimizing unit action, entropy, and information while maximizing their total values are proposed as some of the dynamic variational principles guiding self-organization. The least action principle (LAP) is the proposed driver for self-organization; however, it cannot operate in isolation; it requires the mechanism of feedback loops with the rest of the system's characteristics to drive the process. Average action efficiency (AAE) is introduced as a potential quantitative measure of self-organization, reflecting the system's efficiency as the ratio of events to total action per unit of time. Positive feedback loops link AAE to other system characteristics, potentially explaining power–law relationships, quantity–AAE transitions, and exponential growth patterns observed in complex systems. To explore this framework, we apply it to agent-based simulations of ants navigating between two locations on a 2D grid. The principles align with observed self-organization dynamics, and the results and comparisons with real-world data appear to support the model. By analyzing AAE, this study seeks to address fundamental questions about the nature of self-organization and system organization, such as "Why and how do complex systems self-organize? What is organization and how organized is a system?". We present AAE for the discussed simulation and whenever no external forces act on the system. Given so many specific cases in nature, the method will need to be adapted to reflect their specific interactions. These findings suggest that the proposed models offer a useful perspective for understanding and potentially improving the design of complex systems. [ABSTRACT FROM AUTHOR]

Shale is a common rock in oil and gas extraction, and the study of its nonlinear mechanical behavior is crucial for the development of engineering techniques such as hydraulic fracturing. This paper establishes a new coupled elastic–plastic damage model based on the second law of thermodynamics, the strain equivalence principle, the non-associated flow rule, and the Drucker–Prager yield criterion. This model is used to describe the mechanical behavior of shale before and after peak strength and has been implemented in ABAQUS via UMAT for numerical computation. The model comprehensively considers the quasi-brittle and anisotropic characteristics of shale, as well as the strength degradation caused by damage during both the elastic and plastic phases. A damage yield function has been established as a criterion for damage occurrence, and the constitutive integration algorithm has been derived using a regression mapping algorithm. Compared with experimental data from La Biche shale in Canada, the theoretical model accurately simulated the stress–strain curves and volumetric–axial strain curves of shale under confining pressures of 5 MPa, 25 MPa, and 50 MPa. When compared with experimental data from shale in Western Hubei and Eastern Chongqing, China, the model precisely fitted the stress–strain curves of shale at pressures of 30 MPa, 50 MPa, and 70 MPa, and at bedding angles of 0°, 22.5°, 45°, and 90°. This proves that the model can effectively predict the failure behavior of shale under different confining pressures and bedding angles. Additionally, a sensitivity analysis has been performed on parameters such as the plastic hardening rate b, damage evolution rate Bω, weighting factor r, and damage softening parameter a. This research is expected to provide theoretical support for the efficient extraction technologies of shale oil and gas. [ABSTRACT FROM AUTHOR]

Coal is considered to be one of the most significant energy sources in the world. Dewatering, upgrading, and reutilization of lignite is an essential way for the clean coal utilization. Numerical simulation is a practical method combined experimental data with fundamental theories. In this study, based on the Luikov irreversible thermodynamic model, numerical calculations were carried out using the finite volume method and total Hermite integration. The drying characteristics of lignite at different drying temperatures and airflow velocities were simulated employing the fluid computational software. Initially, in order to verify the reliability of the simulation model, the simulated results were compared and validated with the experimental data. The results indicated that the drying parameters obtained from the simulation were in good agreement with the experimental values, and the correlation coefficients were greater than 0.95. Furthermore, the influence of airflow velocity and temperature on the drying characteristics was analyzed based on the numerical results. The results revealed that the drying temperature had the greatest effect on the drying process, while the airflow velocity had a minor effect. The optimum drying conditions for lignite were in the range of 1.2–1.8 m/s for airflow velocity and in the range of 140–160°C for drying temperature. [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]

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]

We present a review of the Semi-Symmetric Metric Gravity (SSMG) theory, representing a geometric extension of standard general relativity, based on a connection introduced by Friedmann and Schouten in 1924. The semi-symmetric connection is a connection that generalizes the Levi-Civita one by allowing for the presence of a simple form of the torsion, described in terms of a torsion vector. The Einstein field equations are postulated to have the same form as in standard general relativity, thus relating the Einstein tensor constructed with the help of the semi-symmetric connection, with the energy–momentum tensor. The inclusion of the torsion contributions in the field equations has intriguing cosmological implications, particularly during the late-time evolution of the Universe. Presumably, these effects also dominate under high-energy conditions, and thus SSMG could potentially address unresolved issues in general relativity and cosmology, such as the initial singularity, inflation, or the 7Li problem of the Big-Bang Nucleosynthesis. The explicit presence of torsion in the field equations leads to the non-conservation of the energy–momentum tensor, which can be interpreted within the irreversible thermodynamics of open systems as describing particle creation processes. We also review in detail the cosmological applications of the theory, and investigate the statistical tests for several models, by constraining the model parameters via comparison with several observational datasets. [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]

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]

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]

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]

Under complex approach by means of simultaneous measurements (during the deformation) of stress-strain diagrams (τ-ε), the Hall coefficient RH, electrical conductivity σ, temperature dependences of microhardness Нv(Т) and quantitative analysis of interfacial interactions (energy of interfacial interaction γm and interfacial tension σm), the peculiarities of the mechanical properties in CdxHg1-xTe solid-solution crystals (х = 0-0.26) with metal and semi-conductor properties are studied. The special role of point defects and the influence of band structure on the behaviour of mobile dislocations are established. As found, in the process of strain hardening, a significant contribution is made by the interphase interaction between neighbouring structural fragments inherent in the semi-metallic crystal as well as induced in the process of deformation. From the point of view of non-equilibrium thermodynamics, energy parameters of interphase interaction in a fragmented crystal are estimated and a mechanism of self-organization is proposed. The peculiarities of near-surface layers and their role in formation of the elastic-plastic state of the investigated crystals are analysed. As claimed, the crystal under process of deformation should be considered as an open non-equilibrium thermodynamic system that evolves to minimum entropy not only to preserve its integrity, but also to create new types of structures (defects) capable of more effectively dissipating the added energy. [ABSTRACT FROM AUTHOR]

In this article, the linear non-equilibrium thermodynamic approach is used to mathematically describe the energy regularities of an interior permanent magnet synchronous motor (IPMSM), taking into account iron loss. The IPMSM is considered a linear power converter (PC) that is multiple-linearized at operating points with a given angular velocity and load torque. A universal description of such a PC by a system of dimensionless parameters and characteristics made it possible to analyze the perfection of energy conversion in the object. For IPMSM, taking into account iron loss, a mathematical model of the corresponding PC has been built, and an algorithm and research program have been developed, which is valid in a wide range of machine speed regulations. This allows you to choose the optimal points of PC operation according to the maximum efficiency criteria and obtain the efficiency maps for IPMSM in different speed regions. The results of the studies demonstrate the effectiveness of the proposed method for determining the references of the d and q components of the armature current for both the loss-minimization strategy at the constant torque range of motor speed and the flux-weakening strategy in the constant power range. [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]

This paper proposes a simple mathematical model of non-stationary and non-linear stochastic dynamics, which approximates a (globally) non-stationary and non-linear stochastic process by its locally (or 'piecewise') stationary version. Profiting from the elegance and simplicity of both, the exact mathematical model referred to as the Ornstein–Uhlenbeck stochastic process (which is globally stationary, Markov and Gaussian) and of the Lyapunov criterion associated with the stability of stationarity, we show that the proposed non-linear non-stationary model provides a natural extension of the Onsager–Machlup theory of equilibrium thermal fluctuations, to the realm of non-stationary, non-linear and non-equilibrium processes. As an illustrative application, we then apply the extended non-equilibrium Onsager–Machlup theory, to the description of thermal fluctuations and irreversible relaxation processes in liquids, leading to the main exact equations employed to construct the non-equilibrium self-consistent generalised Langevin equation (NE-SCGLE) theory of irreversible processes in liquids. This generic theory has demonstrated that the most intriguing and long-unsolved questions of the glass and gel transitions are understood as a natural consequence of the second law of thermodynamics, enunciated in terms of the proposed piecewise stationary stochastic mathematical model. [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]

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]

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]