The nature takes the easiest and most accessible paths and, hence, processes are accomplished very quickly in a minimum time. In 1662 P. Fermat used this principle to work out the refraction law. This was one of the first known attempts at successful deductive description of a physical phenomenon involving the variational principle. Presently researchers concerned with nonequilibrium processes have turned back to Fermat's idea in the form of the maximum entropy production principle (MEPP). MEPP has proved to be good for understanding and description of diverse nonequilibrium processes in physics, chemistry and biology. This brings up two questions: 1) Can this principle claim to be the basis of all nonequilibrium physics? 2) Is it possible to prove MEPP?
In the paper [Phys.Rev.E Vol.79, 051605 (2009)] by Chou and Pleimling a claim is made that a parameter-free scaling that gives data collapse for some simulation models would replace universal Family-Vicsek (FV) scaling. Here, by giving the explicit form of this scaling for competitive growth models, it is shown that data collapse in this procedure is obtained by a shift-and-scale operator that gives no information about stochastic dynamics and has no relation with FV function.
We prove the nonequilibrium fluctuations of one-dimensional, boundary driven, weakly asymmetric exclusion processes through a microscopic Cole-Hopf transformation.
We generalize nonequilibrium integral equalities to situations involving absolutely irreversible processes for which the forward-path probability vanishes and the entropy production diverges, rendering conventional integral fluctuation theorems inapplicable. We identify the mathematical origins of absolute irreversibility as the singularity of probability measure. We demonstrate the validity of the obtained equalities for several models.
The Zubarev nonequilibrium statistical operator (NSO) method in Renyi statistics is discussed. The solution of $q$-parametrized Liouville equation within the NSO method is obtained. A statistical approach for a consistent description of reaction-diffusion processes in "gas-adsorbate-metal" system is proposed using the NSO method in Renyi statistics.
We obtain hydrodynamic descriptions of a broad class of conserved-mass transport processes on a ring. These processes are governed by chipping, diffusion and coalescence of masses, where microscopic probability weights in their nonequilibrium steady states, having nontrivial correlations, are not known. In these processes, we analytically calculate two transport coefficients, the bulk-diffusion coefficient and the conductivity. We, remarkably, find that the two transport coefficients obey an equilibriumlike Einstein relation, although the microscopic dynamics does not satisfy detailed balance …
Generic inhomogeneous steady states in an asymmetric exclusion process on a ring with a pair of point bottlenecks are studied. We show that, due to an underlying universal feature, measurements of coarse-grained steady-state densities in this model resolve the bottleneck structures only partially. Unexpectedly, it displays localization-delocalization transitions and confinement of delocalized domain walls, controlled by the interplay between particle number conservation and bottleneck competition for moderate particle densities.
In a generalized framework for the Landauer erasure protocol, we study bounds on the heat dissipated in typical nonequilibrium quantum processes. In contrast to thermodynamic processes, quantum fluctuations are not suppressed in the nonequilibrium regime and cannot be ignored, making such processes difficult to understand and treat. Here we derive an emergent fluctuation relation that virtually guarantees the average heat produced to be dissipated into the reservoir either when the system or reservoir is large (or both) or when the temperature is high. The implication of our result is that for…
Given nonstationary data from molecular dynamics simulations, a Markovian Langevin model is constructed that aims to reproduce the time evolution of the underlying process. While at equilibrium the free energy landscape is sampled, nonequilibrium processes can be associated with a biased energy landscape, which accounts for finite sampling effects and external driving. Extending the data-driven Langevin equation (dLE) approach [Phys.\ Rev.\ Lett.\ {\bf 115}, 050602 (2015)] to the modeling of nonequilibrium processes, an efficient way to calculate multidimensional Langevin fields is outlined. T…
We investigate entropy production in finitely slow transitions between nonequilibrium steady states in Markov jump processes using the improved adiabatic approximation method proposed by Takahashi, Fujii, Hino and Hayakawa [1]. This method provides systematic improvement of the adiabatic approximation on infinitely slow transitions from which we obtain nonadiabatic corrections and has a close relationship with the slow driving perturbation [2, 3]. We analyze two types of excess entropy production of Sagawa and Hayakawa [4] and Hatano and Sasa [5] as examples, and confirm that the leading adiab…
Work fluctuation and total entropy production play crucial roles in small thermodynamic systems subject to large thermal fluctuations. We investigate a trade-off relation between them in a nonequilibrium situation in which a system starts from an arbitrary nonequilibrium state. We apply the variational method to study this problem and find a stationary solution against variations over protocols that describe the time dependence of the Hamiltonian of the system. Using the stationary solution, we find the minimum of the total entropy production for a given amount of work fluctuation. An explicit…
I revisit the exactly solvable Kipnis--Marchioro--Presutti model of heat conduction [J. Stat. Phys. 27 65 (1982)] and describe, for one-dimensional systems of arbitrary sizes whose ends are in contact with thermal baths at different temperatures, a systematic characterization of their non-equilibrium stationary states. These arguments avoid resorting to the analysis of a dual process and yield a straightforward derivation of Fourier's law, as well as higher-order static correlations, such as the covariant matrix. The transposition of these results to families of gradient models generalizing th…
The fluctuation theorem, where the central quantity is the work distribution, is an important characterization of nonequilibrium thermodynamics. In this work, based on the dissipaton-equation-of-motion theory, we develop an exact method to evaluate the work distributions in quantum impurity system-bath mixing processes, in the presence of non-Markovian and strong couplings. Our results not only precisely reproduce the Jarzynski equality and Crooks relation, but also reveal rich information on large deviation. The numerical demonstrations are carried out with a spin-boson model system.
Nonequilibrium thermodynamics (NET) investigates processes in systems out of global equilibrium. On a mesoscopic level, it provides a statistical dynamic description of various complex phenomena such as chemical reactions, ion transport, diffusion, thermochemical, thermomechanical and mechanochemical fluxes. In the present review, we introduce a mesoscopic stochastic formulation of NET by analyzing entropy production in several simple examples. The fundamental role of nonequilibrium steady-state cycle kinetics is emphasized. The statistical mechanics of Onsager's reciprocal relations in this c…
Nonequilibrium fluctuation-dissipation theorems (FDTs) are one of the most important advances in stochastic thermodynamics over the past two decades. Here we provide rigorous mathematical proofs of two types of nonequilibrium FDTs for inhomogeneous diffusion processes with unbounded drift and diffusion coefficients by using the Schauder estimates for partial differential equations of parabolic type and the theory of weakly continuous semigroups. The FDTs proved in this paper apply to any forms of inhomogeneous and nonlinear external perturbations. Furthermore, we prove the uniqueness of the co…
Estimating equilibrium ensemble averages using multiple time slices from driven nonequilibrium processes: theory and application to free energies, moments, and thermodynamic length in single-molecule pulling experiments
While originally discovered in the context of the Gaussian Unitary Ensemble, the Tracy-Widom distribution also rules the height fluctuations of growth processes. This suggests that there might be other nonequilibrium processes in which the Tracy-Widom distribution plays an important role. In our contribution we study one-dimensional systems with domain wall initial conditions. For an appropriate choice of parameters the profile develops a rarefaction wave, while maintaining the initial equilibrium states far to the left and right, which thus serve as infinitely extended thermal reservoirs. For…
We consider rapid cooling processes in classical, 3-dimensional, purely repulsive binary mixtures in which an initial infinite-temperature (ideal-gas) configuration is instantly quenched to zero temperature. It is found that such systems display two kinds of ordering processes, the type of which can be controlled by tuning the interactions between unlike particles. While strong inter-species repulsion leads to chemical ordering in terms of an unmixing process, weak repulsion gives rise to spontaneous crystallization, maintaining chemical homogeneity. This result indicates the existence of a tr…
