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A feature of biological systems is their high structural heterogeneity. This is manifested in the fact that the processes observed at the nanoscopic level are noticeably multistage in time. The paper expounds an approach that allows, basing on the methods of nonequilibrium statistical mechanics, to obtain kinetic equations that enable describing the evolution of slow processes occurring against the background of faster ones. Vibrational relaxation in electronic terms and stochastic deviations of the position of the electronic energy levels of the system from their stationary positions are considered the most important fast processes. As an example, it is shown how the kinetics of one- and two-electron transfer through protein chains, the oxygen-mediated transfer of a triplet excitation in the pigment-protein complex, the kinetics of temperature-independent desensitization of pain receptors, as well as conformational regulation of enzymatic reactions, can be described. [ABSTRACT FROM AUTHOR]

The article discusses directed active motion of motor proteins has a vital process in virtually all eukaryotic cells. Topics include the discovery of directionality switching of mitotic kinesin-5 motors challenged the long-standing paradigm that individual kinesin motors have characterized by an intrinsic directionality; and the model shows excellent quantitative agreement with experimental data obtained under high and low ionic strength conditions.

This paper aims at unifying the statistical mechanics and thermodynamics of glass through a new extended definition of temperature. Along with new insights into the Clausius theorem, this definition has been derived from a three-level model system. As previously shown in our study of a two-level system, introduction of an additional parameter, i.e. an internal temperature, is useful to describe the relation between energy and entropy changes in non-equilibrium states. Because a further extension is indispensable to deal with more realistic glass models, we define here temperature as a tensor whose diagonal components, the statistical temperatures, constitute a bridge between thermodynamic variables and a partition function in the framework of non-equilibrium statistical mechanics. On the other hand, the non-diagonal components, named thermodynamic temperatures, are used to extend the Clausius theorem within the framework of non-equilibrium thermodynamics. The new formalism is applied to a three-level model as the simplest example of multilevel system. It succeeds in describing the relation between energy changes and entropy in non-equilibrium states. In addition, this study sheds a new light on the interpretation of the second law of thermodynamics. As a result, Clausius' definition of entropy, and its famous inequality for non-equilibrium cases can be merged into a single equality without the introduction of any additional terms. In addition, this study introduces a more general definition of the zeroth law of thermodynamics for non-equilibrium conditions, and extends the concept of fictive temperature as an order parameter to distinguish non-equilibrium glasses. [ABSTRACT FROM AUTHOR]

Recurrent neural networks (RNNs) are brain-inspired models widely used in machine learning for analyzing sequential data. The present work is a contribution towards a deeper understanding of how RNNs process input signals using the response theory from nonequilibrium statistical mechanics. For a class of continuous-time stochastic RNNs (SRNNs) driven by an input signal, we derive a Volterra type series representation for their output. This representation is interpretable and disentangles the input signal from the SRNN architecture. The kernels of the series are certain recursively defined correlation functions with respect to the unperturbed dynamics that completely determine the output. Exploiting connections of this representation and its implications to rough paths theory, we identify a universal feature - the response feature, which turns out to be the signature of tensor product of the input signal and a natural support basis. In particular, we show that SRNNs, with only the weights in the readout layer optimized and the weights in the hidden layer kept fixed and not optimized, can be viewed as kernel machines operating on a reproducing kernel Hilbert space associated with the response feature. [ABSTRACT FROM AUTHOR]

For a given thermodynamic system, and a given choice of coarse-grained state variables, the knowledge of a force-flux constitutive law is the basis for any nonequilibrium modeling. In the first paper of this series we established how, by a generalization of the classical fluctuation-dissipation theorem (FDT), the structure of a constitutive law is directly related to the distribution of the fluctuations of the state variables. When these fluctuations can be expressed in terms of diffusion processes, one may use Green–Kubo-type coarse-graining schemes to find the constitutive laws. In this paper we propose a coarse-graining method that is valid when the fluctuations are described by means of general Markov processes, which include diffusions as a special case. We prove the success of the method by numerically computing the constitutive law for a simple chemical reaction A ⇄ B A\rightleftarrows B. Furthermore, we show that, for such a system, one cannot find a consistent constitutive law by any Green–Kubo-like scheme. [ABSTRACT FROM AUTHOR]

Understanding the fluctuations by which phenomenological evolution equations with thermodynamic structure can be enhanced is the key to a general framework of nonequilibrium statistical mechanics. These fluctuations provide an idealized representation of microscopic details. We consider fluctuation-enhanced equations associated with Markov processes and elaborate the general recipes for evaluating dynamic material properties, which characterize force-flux constitutive laws, by statistical mechanics. Markov processes with continuous trajectories are conveniently characterized by stochastic differential equations and lead to Green–Kubo-type formulas for dynamic material properties. Markov processes with discontinuous jumps include transitions over energy barriers with the rates calculated by Kramers. We describe a unified approach to Markovian fluctuations and demonstrate how the appropriate type of fluctuations (continuous versus discontinuous) is reflected in the mathematical structure of the phenomenological equations. [ABSTRACT FROM AUTHOR]

Only a subset of degrees of freedom are typically accessible or measurable in real-world systems. As a consequence, the proper setting for empirical modeling is that of partially-observed systems. Notably, data-driven models consistently outperform physics-based models for systems with few observable degrees of freedom; e.g. hydrological systems. Here, we provide an operator-theoretic explanation for this empirical success. To predict a partially-observed system’s future behavior with physics-based models, the missing degrees of freedom must be explicitly accounted for using data assimilation and model parametrization. Data-driven models, in contrast, employ delay-coordinate embeddings and their evolution under the Koopman operator to implicitly model the effects of the missing degrees of freedom. We describe in detail the statistical physics of partial observations underlying data-driven models using novel maximum entropy and maximum caliber measures. The resulting nonequilibrium Wiener projections applied to the Mori–Zwanzig formalism reveal how data-driven models may converge to the true dynamics of the observable degrees of freedom. Additionally, this framework shows how data-driven models infer the effects of unobserved degrees of freedom implicitly, in much the same way that physics models infer the effects explicitly. This provides a unified implicit-explicit modeling framework for predicting partially-observed systems, with hybrid physics-informed machine learning methods combining both implicit and explicit aspects.

We study the thermodynamics of open systems weakly driven out-of-equilibrium by nonconservative and time-dependent forces using the linear regime of stochastic thermodynamics. We make use of conservation laws to identify the potential and nonconservative components of the forces. This allows us to formulate a unified near-equilibrium thermodynamics. For nonequilibrium steady states, we obtain an Onsager theory ensuring nonsingular response matrices that is consistent with phenomenological linear irreversible thermodynamics. For time-dependent driving protocols that do not produce nonconservative forces, we identify the equilibrium ensemble from which Green–Kubo relations are recovered. For arbitrary periodic drivings, the averaged entropy production (EP) is expressed as an independent sum over each driving frequency of non-negative contributions. These contributions are bilinear in the nonconservative and conservative forces and involve a novel generalized Onsager matrix that is symmetric. In the most general case of arbitrary time-dependent drivings, we advance a novel decomposition of the EP rate into two non-negative contributions—one solely due to nonconservative forces and the other solely due to deviation from the instantaneous steady-state—directly implying a minimum EP principle close to equilibrium. This setting reveals the geometric structure of near-equilibrium thermodynamics and generalizes previous approaches to cases with nonconservative forces.

We study linear response theory and entropic fluctuations of finite dimensional non-equilibrium Repeated Interaction Systems (RIS). More precisely, in a situation where the temperatures of the probes can take a finite number of different values, we prove analogs of the Green–Kubo fluctuation–dissipation formula and Onsager reciprocity relations on energy flux observables. Then we prove a Large Deviation Principle, or Fluctuation Theorem, and a Central Limit Theorem on the full counting statistics of entropy fluxes. We consider two types of non-equilibrium RIS: either the temperatures of the probes are deterministic and arrive in a cyclic way, or the temperatures of the probes are described by a sequence of i.i.d. random variables with uniform distribution over a finite set. [ABSTRACT FROM AUTHOR]

The theory of transport phenomena in multicomponent electrolyte solutions is presented here through the integration of continuum mechanics, electromagnetism, and nonequilibrium thermodynamics. The governing equations of irreversible thermodynamics, including balance laws, Maxwell's equations, internal entropy production, and linear laws relating the thermodynamic forces and fluxes, are derived. Green–Kubo relations for the transport coefficients connecting electrochemical potential gradients and diffusive fluxes are obtained in terms of the flux–flux time correlations. The relationship between the derived transport coefficients and those of the Stefan–Maxwell and infinitely dilute frameworks are presented, and the connection between the transport matrix and experimentally measurable quantities is described. To exemplify the application of the derived Green–Kubo relations in molecular simulations, the matrix of transport coefficients for lithium and chloride ions in dimethyl sulfoxide is computed using classical molecular dynamics and compared with experimental measurements. [ABSTRACT FROM AUTHOR]

In this paper, continuous-time master equations with finite states employed in nonequilibrium statistical mechanics are formulated in the language of discrete geometry. In this formulation, chains in algebraic topology are used, and master equations are described on graphs that consist of vertices representing states and of directed edges representing transition matrices. It is then shown that master equations under the detailed balance conditions are equivalent to discrete diffusion equations, where the Laplacians are defined as self-adjoint operators with respect to introduced inner products. An isospectral property of these Laplacians is shown for non-zero eigenvalues, and its applications are given. The convergence to the equilibrium state is shown by analyzing this class of diffusion equations. In addition, a systematic way to derive closed dynamical systems for expectation values is given. For the case that the detailed balance conditions are not imposed, master equations are expressed as a form of a continuity equation. [ABSTRACT FROM AUTHOR]

The article provides information on a study which examined first-order synchronization transition in a large population of strongly coupled relaxation oscillators. Topics discussed include description on chemical micro-oscillators, role of natural frequency distribution, and synchronization mechanism for relaxation oscillators.

This article presents an idealized mathematical model of the cerebral cortex, focusing on the dynamical interaction of neurons. The author proposes a network architecture more consistent with neuroanatomy than in previous studies, borrows ideas from nonequilibrium statistical mechanics and calls attention to the fact that the brain is a large and complex dynamical system. The ideas proposed are illustrated with a realistic model of the visual cortex. [ABSTRACT FROM AUTHOR]

In this paper we discuss a family of models of particle and energy diffusion on a one-dimensional lattice, related to those studied previously in Sasamoto and Wadati (Phys Rev E 58:4181–4190, 1998), Barraquand and Corwin (Probab Theory Relat Fields 167(3–4):1057–1116, 2017) and Povolotsky (J Phys A 46(46):465205, 2013) in the context of KPZ universality class. We show that they may be mapped onto an integrable sl (2) Heisenberg spin chain whose Hamiltonian density in the bulk has been already studied in the AdS/CFT and the integrable system literature. Using the quantum inverse scattering method, we study various new aspects, in particular we identify boundary terms, modeling reservoirs in non-equilibrium statistical mechanics models, for which the spin chain (and thus also the stochastic process) continues to be integrable. We also show how the construction of a "dual model" of probability theory is possible and useful. The fluctuating hydrodynamics of our stochastic model corresponds to the semiclassical evolution of a string that derives from correlation functions of local gauge invariant operators of N = 4 super Yang–Mills theory (SYM), in imaginary-time. As any stochastic system, it has a supersymmetric completion that encodes for the thermal equilibrium theorems: we show that in this case it is equivalent to the sl (2 | 1) superstring that has been derived directly from N = 4 SYM. [ABSTRACT FROM AUTHOR]

Persistence is defined as the probability that the local value of a fluctuating field remains at a particular state for a certain amount of time, before being switched to another state. The concept of persistence has been found to have many diverse practical applications, ranging from non-equilibrium statistical mechanics to financial dynamics to distribution of time scales in turbulent flows and many more. In this study, we carry out a detailed analysis of the statistical characteristics of the persistence probability density functions (PDFs) of velocity and temperature fluctuations in the surface layer of a convective boundary layer using a field-experimental dataset. Our results demonstrate that for the time scales smaller than the integral scales, the persistence PDFs of turbulent velocity and temperature fluctuations display a clear power-law behavior, associated with a self-similar eddy cascading mechanism. Moreover, we also show that the effects of non-Gaussian temperature fluctuations act only at those scales that are larger than the integral scales, where the persistence PDFs deviate from the power-law and drop exponentially. Furthermore, the mean time scales of the negative temperature fluctuation events persisting longer than the integral scales are found to be approximately equal to twice the integral scale in highly convective conditions. However, with stability, this mean time scale gradually decreases to almost being equal to the integral scale in the near-neutral conditions. Contrarily, for the long positive temperature fluctuation events, the mean time scales remain roughly equal to the integral scales, irrespective of stability. [ABSTRACT FROM AUTHOR]

The Mori–Zwanzig projection operator formalism is one of the central tools of nonequilibrium statistical mechanics, allowing one to derive macroscopic equations of motion from the microscopic dynamics through a systematic coarse-graining procedure. It is important as a method in the physical sciences and gives many insights into the general structure of nonequilibrium transport equations and the general procedure of microscopic derivations. Therefore, it is a valuable ingredient of basic and advanced courses in statistical mechanics. However, accessible introductions to this method—in particular in its more advanced forms—are extremely rare. In this article, we give a simple and systematic introduction to the Mori–Zwanzig formalism, which allows students to understand the methodology in the form it is used in current research. This includes both basic and modern versions of the theory. Moreover, we relate the formalism to more general aspects of statistical mechanics and quantum mechanics. Thereby, we explain how this method can be incorporated into a lecture course on statistical mechanics as a way to give a general introduction to the study of nonequilibrium systems. Applications, in particular to spin relaxation and dynamical density functional theory, are also discussed. [ABSTRACT FROM AUTHOR]

Continuous attractors have been used to understand recent neuroscience experiments where persistent activity patterns encode internal representations of external attributes like head direction or spatial location. However, the conditions under which the emergent bump of neural activity in such networks can be manipulated by space and time-dependent external sensory or motor signals are not understood. Here, we find fundamental limits on how rapidly internal representations encoded along continuous attractors can be updated by an external signal. We apply these results to place cell networks to derive a velocity-dependent nonequilibrium memory capacity in neural networks. [ABSTRACT FROM AUTHOR]

The purpose of this note is two-fold: A) We give a brief introduction into the problem of rigorously justifying the fundamental equations of wave turbulence theory (the theory of nonequilibrium statistical mechanics of nonlinear waves), and B) we describe a recent work of the authors in which they obtain the so-called wave kinetic equation , predicted in wave turbulence theory, for the nonlinear Schrödinger equation on short but nontrivial time scales. [ABSTRACT FROM AUTHOR]

The field of sub-Riemannian geometry has flourished in the past four decades through the strong interactions between problems arising in applied science (in areas such as robotics) and questions of a pure mathematical character about the nature of space. Methods of control theory, such as controllability properties determined by Lie brackets of vector fields, the Hamilton equations associated to the Maximum Principle of optimal control, Hamilton-Jacobi-Bellman equation etc. have all been found to be basic tools for answering such questions. In this paper, we find a useful role for the vantage point of sub-Riemannian geometry in attacking a problem of interest in non-equilibrium statistical mechanics: how does one create rules for operation of micro- and nano-scale systems (heat engines) that are subject to fluctuations from the surroundings, so as to be able to do useful things such as converting heat into work over a cycle of operation? We exploit geometric optimal control theory to produce such rules selected for maximal efficiency. This is done by working concretely with a model problem, the stochastic oscillator. Essential to our work is a separation of time scales used with great efficacy by physicists and justified in the linear response regime. [ABSTRACT FROM AUTHOR]

We review the concept of dynamical ensembles in nonequilibrium statistical mechanics as specified from an action functional or Lagrangian on spacetime. There, under local detailed balance, the breaking of time-reversal invariance is quantified via the entropy flux, and we revisit some of the consequences for fluctuation and response theory. Frenesy is the time-symmetric part of the path-space action with respect to a reference process. It collects the variable quiescence and dynamical activity as function of the system's trajectory, and as has been introduced under different forms in studies of nonequilibria. We discuss its various realizations for physically inspired Markov jump and diffusion processes and why it matters a good deal for nonequilibrium physics. This review then serves also as an introduction to the exploration of frenetic contributions in nonequilibrium phenomena. [ABSTRACT FROM AUTHOR]

We derive a theoretical framework for the non-Newtonian viscosity of a sticky, attractive colloidal dispersion via active microrheology by modeling detailed microscopic attractive and Brownian forces between particles. Actively forcing a probe distorts the surrounding arrangement of particles from equilibrium; the degree of this distortion is characterized by the Péclet number, Pe ≡ F ext / (2 kT / a) , where kT is the thermal energy and a the probe size. Similarly, the strength of attractive interactions relative to Brownian motion is captured by the second virial coefficient, B 2 . We formulate a Smoluchowski equation governing the pair configuration as it evolves with external and attractive forces. The microviscosity is then computed via non-equilibrium statistical mechanics. For active probe forcing, the familiar hard-sphere boundary-layer and wake structures emerge as Pe grows strong, but attractions alter its shape: changes in relative probe motion arising from its attraction to the bath particles can lead to a high- Pe , strong-attraction flipping of the microstructure, where an upstream depletion boundary layer forms, along with a downstream accumulation wake. This highly distorted structure is analyzed at the micro-mechanical level, where changes in the time spent upstream or downstream from a bath particle lead to hypo- and hyper-viscosity. When attractions are strong, separating the interparticle microviscosity into contributions from attractions and repulsions reveals an attractive undershoot and a repulsive overshoot, as advection grows strong enough to break interparticle bonds downstream and drain the wake. In contrast to linear-response rheology that is predictable entirely by B 2 for short-ranged attractions, here the non-Newtonian viscosity is not, owing to the additional length scale introduced by the boundary layer. The ratio of external to attractive forces eventually supersedes B 2 as the relevant predictor of structure and rheology. This behavior may provide interesting connections to active motion in biological systems where attractive forces are present. [ABSTRACT FROM AUTHOR]

In this paper I propose an interpretation of classical statistical mechanics that centers on taking seriously the idea that probability measures represent complete states of statistical mechanical systems. I show how this leads naturally to the idea that the stochasticity of statistical mechanics is associated directly with the observables of the theory rather than with the microstates (as traditional accounts would have it). The usual assumption that microstates are representationally significant in the theory is therefore dispensable, a consequence which suggests interesting possibilities for developing non-equilibrium statistical mechanics and investigating inter-theoretic answers to the foundational questions of statistical mechanics. [ABSTRACT FROM AUTHOR]

The descriptive analysis for the very long-term behavior of the Euro/ALL exchange rates has identified a near to average. revert behavior which contradict some econometric arguments and economical level of the country. Apparent anxious regimes have continuously ended up without crashing and generally the national currency of the not competitive economy has shown a nearly stabilized dynamics toward EU currency. Some of those properties have been explained herein by employing the analysis of the system from complexity and econo-physics point of view. So, by approaching the trend we obtained that the time precursor is characterized by local self-organization regimes that never organized in long scale to produce dangerous move. Thermodynamic-like processes have acted constantly as stabilizer of the national currency value. More details and features have been considered by analyzing the distributions and multifractal structure of the series in the framework of the non-equilibrium statistical mechanics approach. Gathering the information about the stationarity of the states, presences of regimes and their properties, we realized to identify the optimal condition for measurement, modeling and steadfast descriptive statistics. Finally, by using neural network we have realized a forecasting example for one month time interval. The work aims to reveal the importance of interdisciplinary consideration for better results in the study of complex socioeconomic systems. [ABSTRACT FROM AUTHOR]

The mixed quantum-classical formulation derived in our companion paper [D. Bousquet, K. H. Hughes, D. Micha, and I. Burghardt, J. Chem. Phys. 134, 064116 (2011)], which is based upon a hydrodynamic representation of the classical sector, is applied to nonequilibrium nonpolar solvation dynamics as exemplified by the solvation of the electronically excited NO molecule in a rare gas environment. Derived from a partition of the Hamiltonian into a primary (quantum) part and a secondary (classical) part the hydrodynamic equations are formulated for multi-quantum states and result in explicit equations of motion for populations and coherences. The hierarchy of hydrodynamic equations is truncated by the following approximate closure schemes: Gauss-Hermite closure, dynamical density functional theory approximation, and a generalized Maxwellian closure. A comparison of the dynamics using these three closure methods showed that the suitability of a particular closure scheme was dependent on the initial conditions and the nonequilibrium character of the dynamics. [ABSTRACT FROM AUTHOR]

Dynamic and structural properties of biological polymers are important to their function but it is difficult to obtain information on molecular flexibility at an atomic level. This paper describes how a normal mode analysis can be used to describe the equilibrium and nonequilibrium properties of complex polymer systems such as DNA in solution. A weak coupling between the chain deformation and the local chain orientation simplifies the calculations. A crossover in the normal mode behavior is proposed with a transition from straight rod bend modes to longitudinal oscillations of a coil conformation as a function of the stiffness and the degree of polymerization. [ABSTRACT FROM AUTHOR]

The escape of polymer chains from an attractive channel under external electrical field is studied using dynamical Monte Carlo method. Though the escaping process is nonequilibrium in nature, results show that the one-dimensional diffusion theoretical model based on the equilibrium assumption can describe the dependence of the average escaping time (τ0) on the polymer-channel interaction (&eh;), the electrical field (E), the chain length (n), and the channel length (L), qualitatively. Results indicate that both &eh; and E play very important roles in the escaping dynamics. For small &eh;, the polymer chain moves out of the channel continuously and quickly. While for large &eh;, the polymer chain is difficult to move out of long channels as it is trapped for a long time (τtrap) when the end segment is near the critical point xC. These results are consistent with the theoretical results for the free energy profiles at small &eh; and large &eh;, respectively. The dependence of xC and τtrap on &eh; and E are discussed, and specific relations are obtained. The configurational properties of polymer chain are also investigated during the escaping process. [ABSTRACT FROM AUTHOR]

The mechanism of directed substrate-parallel motion of molecules caused by photoinduced potential energy fluctuations is investigated. Unlike simplistic models (e.g., an on-off ratchet), the approach suggested implies that the necessary asymmetry of the potential energy can arise not only from the asymmetry of the substrate potential but also from an asymmetric distribution of the fluctuating charge density in the molecule. The thus induced asymmetry of the potential energy governs the direction motion and enables, under certain conditions, its reversal at some frequencies of resonant laser pulses or temperature. These inferences are exemplified by the model charge distributions in the molecule and substrate, and the charge density fluctuations which are obtained by quantum chemical calculations for the realistic molecule of a substituted phenylpyrene compound on a model substrate. [ABSTRACT FROM AUTHOR]

The nonequilibrium fluctuation theorems have paved the way for estimating equilibrium thermodynamic properties, such as free energy differences, using trajectories from driven nonequilibrium processes. While many statistical estimators may be derived from these identities, some are more efficient than others. It has recently been suggested that trajectories sampled using a particular time-dependent protocol for perturbing the Hamiltonian may be analyzed with another one. Choosing an analysis protocol based on the nonequilibrium density was empirically demonstrated to reduce the variance and bias of free energy estimates. Here, we present an alternate mathematical formalism for protocol postprocessing based on the Feynmac-Kac theorem. The estimator that results from this formalism is demonstrated on a few low-dimensional model systems. It is found to have reduced bias compared to both the standard form of Jarzynski's equality and the previous protocol postprocessing formalism. [ABSTRACT FROM AUTHOR]

We introduce a new forward flux sampling in time algorithm to efficiently measure transition times in rare-event processes in nonequilibrium systems and apply it to study the first-order (discontinuous) kinetic transition in the Ziff-Gulari-Barshad model of catalytic surface reaction. The average time for the transition to take place, as well as both the spinodal and transition points, is efficiently found by this method. [ABSTRACT FROM AUTHOR]

We developed a general framework to quantify three key ingredients for dynamics of nonequilibrium systems through path integrals in length space. First, we identify dominant kinetic paths as the ones with optimal weights, leading to effective reduction of dimensionality or degrees of freedom from exponential to polynomial so large systems can be treated. Second, we uncover the underlying nonequilibrium potential landscapes from the explorations of the state space through kinetic paths. We apply our framework to a specific example of nonequilibrium network system: lambda phage genetic switch. Two distinct basins of attractions emerge. The dominant kinetic paths from one basin to another are irreversible and do not follow the usual steepest descent or gradient path along the landscape. It reflects the fact that the dynamics of nonequilibrium systems is not just determined by potential gradient but also the residual curl flux force, suggesting experiments to test theoretical predictions. Third, we have calculated dynamic transition time scales from one basin to another critical for stability of the system through instantons. Theoretical predictions are in good agreements with wild type and mutant experiments. We further uncover the correlations between the kinetic transition time scales and the underlying landscape topography: the barrier heights along the dominant paths. We found that both the dominant paths and the landscape are relatively robust against the influences of external environmental perturbations and the system tends to dissipate less with less fluctuations. Our general framework can be applied to other nonequilibrium systems. [ABSTRACT FROM AUTHOR]

In many dynamical systems, there is a large separation of time scales between typical events and 'rare' events which can be the cases of interest. Rare-event rates are quite difficult to compute numerically, but they are of considerable practical importance in many fields, for example, transition times in chemical physics and extinction times in epidemiology can be very long, but are quite important. We present a very fast numerical technique that can be used to find long transition times (very small rates) in low-dimensional systems, even if they lack detailed balance. We illustrate the method for a bistable nonequilibrium system introduced by Maier and Stein and a two-dimensional (in parameter space) epidemiology model. [ABSTRACT FROM AUTHOR]

We investigate the properties of local spin current and local spin density in a tubular two-dimensional electron gas system with Rashba spin-orbit coupling. To evaluate the spatial distribution of the spin-related quantities in both equilibrium and nonequilibrium cases, we derive the tubular version of tight-binding model and then employ the Landauer–Keldysh formalism. Our work reveals that the tubular geometry effect can cause spin-orbit-induced phenomena very different from those in a planar sample. In particular, a persistent spin current circulating in the tubular system is found to be robust against the disorder, thus suggesting its observability. In spite of the absence of spin accumulation, the spin Hall current can still arise and even circulate in the tubular sample. Moreover, a spin-independent impurity will induce distinctive spin accumulation patterns around the impurity, which may serve as a novel mechanism to control electron spins by arranging the impurities for spintronic devices. [ABSTRACT FROM AUTHOR]

It has recently become apparent that the dissipation function, first defined by Evans and Searles [J. Chem. Phys. 113, 3503 (2000)], is one of the most important functions in classical nonequilibrium statistical mechanics. It is the argument of the Evans–Searles fluctuation theorem, the dissipation theorem, and the relaxation theorems. It is a function of both the initial distribution and the dynamics. We pose the following question: How does the dissipation function change if we define that function with respect to the time evolving phase space distribution as one relaxes from the initial equilibrium distribution toward the nonequilibrium steady state distribution? We prove that this covariant dissipation function has a rather simple fixed relationship to the dissipation function defined with respect to the initial distribution function. We also show that there is no exact, time-local, Evans–Searles nonequilibrium steady state fluctuation relation for deterministic systems. Only an asymptotic version exists. [ABSTRACT FROM AUTHOR]

Chemical master equations provide a mathematical description of stochastic reaction kinetics in well-mixed conditions. They are a valid description over length scales that are larger than the reactive mean free path and thus describe kinetics in compartments of mesoscopic and macroscopic dimensions. The trajectories of the stochastic chemical processes described by the master equation can be ensemble-averaged to obtain the average number density of chemical species, i.e., the true concentration, at any spatial scale of interest. For macroscopic volumes, the true concentration is very well approximated by the solution of the corresponding deterministic and macroscopic rate equations, i.e., the macroscopic concentration. However, this equivalence breaks down for mesoscopic volumes. These deviations are particularly significant for open systems and cannot be calculated via the Fokker–Planck or linear-noise approximations of the master equation. We utilize the system-size expansion including terms of the order of Ω-1/2 to derive a set of differential equations whose solution approximates the true concentration as given by the master equation. These equations are valid in any open or closed chemical reaction network and at both the mesoscopic and macroscopic scales. In the limit of large volumes, the effective mesoscopic rate equations become precisely equal to the conventional macroscopic rate equations. We compare the three formalisms of effective mesoscopic rate equations, conventional rate equations, and chemical master equations by applying them to several biochemical reaction systems (homodimeric and heterodimeric protein-protein interactions, series of sequential enzyme reactions, and positive feedback loops) in nonequilibrium steady-state conditions. In all cases, we find that the effective mesoscopic rate equations can predict very well the true concentration of a chemical species. This provides a useful method by which one can quickly determine the regions of parameter space in which there are maximum differences between the solutions of the master equation and the corresponding rate equations. We show that these differences depend sensitively on the Fano factors and on the inherent structure and topology of the chemical network. The theory of effective mesoscopic rate equations generalizes the conventional rate equations of physical chemistry to describe kinetics in systems of mesoscopic size such as biological cells. [ABSTRACT FROM AUTHOR]

Thirty years ago, Jaynes suggested a general theoretical approach to nonequilibrium statistical mechanics, called maximum caliber (MaxCal) [Annu. Rev. Phys. Chem. 31, 579 (1980)]. MaxCal is a variational principle for dynamics in the same spirit that maximum entropy is a variational principle for equilibrium statistical mechanics. Motivated by the success of maximum entropy inference methods for equilibrium problems, in this work the MaxCal formulation is applied to the inference of nonequilibrium processes. That is, given some time-dependent observables of a dynamical process, one constructs a model that reproduces these input data and moreover, predicts the underlying dynamics of the system. For example, the observables could be some time-resolved measurements of the folding of a protein, which are described by a few-state model of the free energy landscape of the system. MaxCal then calculates the probabilities of an ensemble of trajectories such that on average the data are reproduced. From this probability distribution, any dynamical quantity of the system can be calculated, including population probabilities, fluxes, or waiting time distributions. After briefly reviewing the formalism, the practical numerical implementation of MaxCal in the case of an inference problem is discussed. Adopting various few-state models of increasing complexity, it is demonstrated that the MaxCal principle indeed works as a practical method of inference: The scheme is fairly robust and yields correct results as long as the input data are sufficient. As the method is unbiased and general, it can deal with any kind of time dependency such as oscillatory transients and multitime decays. [ABSTRACT FROM AUTHOR]

By using nonequilibrium Green’s functions in combination with the density-functional theory, we investigate the electronic transport properties in a bimolecular device, which is substituted by two amino groups or two nitro groups. The results show that the side groups can modulate the transport properties by their substituted position. The current of the system substituted by two amino groups on the same side is bigger than that on the different side. Contrarily, the current of the system substituted by two nitro groups on the same side is smaller than that on the different side. More importantly, the negative differential resistance (NDR) behavior can be observed only when the system substituted by two amino groups on the same side. The mechanisms are proposed for the effect of the side groups and NDR behavior. [ABSTRACT FROM AUTHOR]

We have conducted a triple-scale simulation of liquid water by concurrently coupling atomistic, mesoscopic, and continuum models of the liquid. The presented triple-scale hydrodynamic solver for molecular liquids enables the insertion of large molecules into the atomistic domain through a mesoscopic region. We show that the triple-scale scheme is robust against the details of the mesoscopic model owing to the conservation of linear momentum by the adaptive resolution forces. Our multiscale approach is designed for molecular simulations of open domains with relatively large molecules, either in the grand canonical ensemble or under nonequilibrium conditions. [ABSTRACT FROM AUTHOR]

Existing optimal estimators of nonequilibrium path-ensemble averages are shown to fall within the framework of extended bridge sampling. Using this framework, we derive a general minimal-variance estimator that can combine nonequilibrium trajectory data sampled from multiple path-ensembles to estimate arbitrary functions of nonequilibrium expectations. The framework is also applied to obtain asymptotic variance estimates, which are a useful measure of statistical uncertainty. In particular, we develop asymptotic variance estimates pertaining to Jarzynski’s equality for free energies and the Hummer–Szabo expressions for the potential of mean force, calculated from uni- or bidirectional path samples. These estimators are demonstrated on a model single-molecule pulling experiment. In these simulations, the asymptotic variance expression is found to accurately characterize the confidence intervals around estimators when the bias is small. Hence, the confidence intervals are inaccurately described for unidirectional estimates with large bias, but for this model it largely reflects the true error in a bidirectional estimator derived by Minh and Adib. [ABSTRACT FROM AUTHOR]

We present the studies of energy and momentum relaxation dynamics of nonequilibrium holes in GaxIn1-xNyAs1-y/GaAs quantum well modulation doped with Be. Experimental results show that the real-space transfer (RST) of hot holes occurs via thermionic emission from the high-mobility GaInNAs quantum wells into the low-mobility GaAs barriers at a threshold electric field of F∼6 kV/cm at T=13 K. At this field the hole drift velocity saturates at vd∼1×107 cm/s. A slight increase in the field above the threshold leads to the impact ionization of acceptors in the barriers by the nonequilibrium holes. We observe and model theoretically a negative differential mobility effect induced by RST that occurs at an electric field of F∼7 kV/cm. The observed current surge at electric fields above 7 kV/cm is attributed to the hole multiplication induced by shallow impurity breakdown in the GaAs barrier and impact ionization in the high-field domain regime associated with the packet of RST of holes in the well. [ABSTRACT FROM AUTHOR]

The general form for the probability density and for the transition probability of a nonequilibrium system is given. Maximization of the latter gives a generalized fluctuation-dissipation theorem by providing a molecular basis for Langevin’s friction force that avoids continuum hydrodynamics. The result shows that the friction coefficient must be proportional to the variance of the stochastic equations of motion. Setting the variance to zero but keeping the friction coefficient nonzero reduces the theory to a Hoover thermostat without explicit constraint, although such a limit violates the physical requirement of proportionality between the dissipation and the fluctuation. A stochastic molecular dynamics algorithm is developed for both equilibrium and nonequilibrium systems, which is tested for steady heat flow and for a time-varying, driven Brownian particle. [ABSTRACT FROM AUTHOR]

We present a theory for Raman scattering by current-carrying molecular junctions. The approach combines a nonequilibrium Green’s function (NEGF) description of the nonequilibrium junction with a generalized scattering theory formulation for evaluating the light scattering signal. This generalizes our previous study [M. Galperin and A. Nitzan, Phys. Rev. Lett. 95, 206802 (2005); J. Chem. Phys. 124, 234709 (2006)] of junction spectroscopy by including molecular vibrations and developing machinery for calculation of state-to-state (Raman scattering) fluxes within the NEGF formalism. For large enough voltage bias, we find that the light scattering signal contains, in addition to the normal signal associated with the molecular ground electronic state, also a contribution from the inverse process originated from the excited molecular state as well as an interference component. The effects of coupling to the electrodes and of the imposed bias on the total Raman scattering as well as its components are discussed. Our result reduces to the standard expression for Raman scattering in the isolated molecule case, i.e., in the absence of coupling to the electrodes. The theory is used to discuss the charge-transfer contribution to surface enhanced Raman scattering for molecules adsorbed on metal surfaces and its manifestation in the biased junction. [ABSTRACT FROM AUTHOR]

We demonstrate how the surrogate process approximation (SPA) method can be used to compute both the potential of mean force along a reaction coordinate and the associated diffusion coefficient using a relatively small number (10–20) of bidirectional nonequilibrium trajectories coming from a complex system. Our method provides confidence bands which take the variability of the initial configuration of the high-dimensional system, continuous nature of the work paths, and thermal fluctuations into account. Maximum-likelihood-type methods are used to estimate a stochastic differential equation (SDE) approximating the dynamics. For each observed time series, we estimate a new SDE resulting in a collection of SPA models. The physical significance of the collection of SPA models is discussed and methods for exploiting information in the population of estimated SPA models are demonstrated and suggested. Molecular dynamics simulations of potassium ion dynamics inside a gramicidin A channel are used to demonstrate the methodology, although SPA-type modeling has also proven useful in analyzing single-molecule experimental time series [J. Phys. Chem. B 113, 118 (2009)]. [ABSTRACT FROM AUTHOR]