P. Ván
How can we derive the evolution equations of dissipative systems? What is the relation between the different approaches? How much do we understand the fundamental aspects of a second law based framework? Is there a hierarchy of dissipative and ideal theories at all? How far can we reach with the new methods of nonequilibrium thermodynamics?
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A new approach - nonequilibrium evolution thermodynamics, is compared with classical variant of Landau approach
Twentyseven comments (.) on the Second Law and nonequilibrium systems
The thermodynamics is studied with the thermodynamic parameter of the lifetime, first-passage time, generalizing the equilibrium thermodynamics. Various ways of describing several stationary nonequilibrium states in the system are considered. The possibilities of increasing the lifetime of the system under external influences on it are investigated.
A thermodynamic expression for the analog of the canonical ensemble for nonequilibrium systems is described based on a purely information theoretical interpretation of entropy. As an application, it is shown that this nonequilibrium canonical distribution implies some important results from nonequilibrium thermodynamics, specifically, the fluctuation theorem and the Jarzynski-equality.
Emergent Second Law for Time-Dependent Nonequilibrium States
针对非自治开放系统，推导了约束时间依赖宏观涨落的涌现第二定律，将McLennan-Zubarev公式推广至弱非保守亲和性的非自治系统，并在双稳态系统中验证了结果。
Aspects of the modern dynamical systems approach to thermodynamics of stationary states out of equilibrium with attention to the original conceptions which arose at the beginnings of Statistical Mechanics
A variant of continuous nonequilibrium thermodynamic theory based on the postulate of the scale invariance of the local relation between generalized fluxes and forces has been proposed. This single postulate replaces the assumptions on local equilibrium and on the known relation between thermodynamic fluxes and forces, which are widely used in classical nonequilibrium thermodynamics. It has been shown that such a modification not only makes it possible to deductively obtain the main results of classical linear nonequilibrium thermodynamics, but also provides a number of statements for a nonlin…
Chemical reaction networks (CRNs) are prototypical complex systems because reactions are nonlinear and connected in intricate ways, and they are also essential to understand living systems. Here, I discuss how recent developments in nonequilibrium thermodynamics provide new insight on how CRNs process energy and perform sophisticated tasks, and describe open challenges in the field.
Nonequilibrium work-Hamiltonian connection for a microstate plays a central role in diverse branches of statistical thermodynamics (fluctuation theorems, quantum thermodynamics, stochastic thermodynamics, etc.). We show that the change in the Hamiltonian for a microstate should be identified with the work done by it, and not the work done on it. This contradicts the current practice in the field. The difference represents a contribution whose average gives the work that is dissipated due to irreversibility. As the latter has been overlooked, the current identification does not properly account…
To describe the nonequilibrium states of the system, a new thermodynamic parameter - system lifetime - is introduced. Statistical distributions that describe the behavior of energy and lifetime are recorded. Entropy and obtained thermodynamic relations are compared with the results of Extended Irreversible thermodynamics, where as an additional parameter selected fluxes. For the case of thermal conductivity explicit expressions are obtained for average lifetime and conjugate thermodynamic quantity. It is shown that near the equilibrium state, when is only one stationary nonequilibrium state, f…
We establish the foundations of a nonequilibrium theory of quantum thermodynamics for noninteracting open quantum systems strongly coupled to their reservoirs within the framework of the nonequilibrium Green functions (NEGF). The energy of the system and its coupling to the reservoirs are controlled by a slow external time-dependent force treated to first order beyond the quasistatic limit. We derive the four basic laws of thermodynamics and characterize reversible transformations. Stochastic thermodynamics is recovered in the weak coupling limit.
Development of thermodynamic induction up to second order gives a dynamical bifurcation for thermodynamic variables and allows for the prediction and detailed explanation of nonequilibrium phase transitions with associated spontaneous symmetry breaking. By taking into account nonequilibrium fluctuations, long range order is analyzed for possible pattern formation. Consolidation of results up to second order produces thermodynamic potentials that are maximized by stationary states of the system of interest. These new potentials differ from the traditional thermodynamic potentials. In particular…
The relation between thermostats of "isoenergetic" and "frictionless" kind is studied and their equivalence in the thermodynamic limit is proved in space dimension $d=1,2$ and, for special geometries, $d=3$.
Nonequilibrium Third Law of Thermodynamics
本文综述非平衡热力学第三定律研究，并以马尔可夫跳跃过程首次到达其他状态的平均时间重新解释准势，为非平衡热容计算提供新视角。
Master equation could be applied to model various kinds of biochemical systems. A general theory for its time-dependent nonequilibrium thermodynamics is rigorously derived. We not only introduce a concept of general internal energy, but also propose an extension of the equilibrium state. Moreover, we find out an explicit expression for the extended form of the Second Law, which is phenomenologically stated as "the conversion of work to excess heat is irreversible". The theory is carefully applied to several thermodynamic processes, and its consistence with the classical thermodynamics is clear…
We compare two approaches to nonequilibrium thermodynamics, the two-generator bracket formulation of time-evolution equations for averages and the macroscopic fluctuation theory, for an isothermal driven diffusive system under steady state conditions. The fluctuation dissipation relations of both approaches play an important role for a detailed comparison. The nonequilibrium Helmholtz free energies introduced in these two approaches differ as a result of boundary conditions. A Fokker-Planck equation derived by projection operator techniques properly reproduces long range fluctuations in nonequ…
Current formulations of nonequilibrium thermodynamics of open chemical reaction networks only consider chemostats as free-energy sources sustaining nonequilibrium behaviours. Here, we extend the theory to include incoherent light as a source of free energy. We do so by relying on a local equilibrium assumption to derive the chemical potential of photons relative to the system they interact with. This allows us to identify the thermodynamic potential and the thermodynamic forces driving light-reacting chemical systems out of equilibrium. We use this framework to treat two paradigmatic photochem…
We show that systems driven by an external force and described by Nose-Hoover dynamics allow for a consistent nonequilibrium thermodynamics description when the thermostatted variable is initially assumed in a state of canonical equilibrium. By treating the "real" variables as the system and the thermostatted variable as the reservoir, we establish the first and second law of thermodynamics. As for Hamiltonian systems, the entropy production can be expressed as a relative entropy measuring the system-reservoir correlations established during the dynamics.
Comparison of extended irreversible thermodynamics and nonequilibrium statistical operator method with thermodynamics based on a distribution containing the first-passage time
本文对比了包含首达时间参数的分布版非平衡热力学、非平衡统计算子方法与扩展不可逆热力学，将扩展不可逆热力学的弛豫时间τ替换为平均首达时间，并推导了相关热力学参数的表达式。
In this work, we analyze the nonequilibrium thermodynamics of a class of neural networks known as Restricted Boltzmann Machines (RBMs) in the context of unsupervised learning. We show how the network is described as a discrete Markov process and how the detailed balance condition and the Maxwell-Boltzmann equilibrium distribution are sufficient conditions for a complete thermodynamics description, including nonequilibrium fluctuation theorems. Numerical simulations in a fully trained RBM are performed and the heat exchange fluctuation theorem is verified with excellent agreement to the theory.…
In previous papers we have introduced a natural nonequilibrium free energy by considering the functional describing the large fluctuations of stationary nonequilibrium states. While in equilibrium this functional is always convex, in nonequilibrium this is not necessarily the case. We show that in nonequilibrium a new type of singularities can appear that are interpreted as phase transitions. In particular, this phenomenon occurs for the one-dimensional boundary driven weakly asymmetric exclusion process when the drift due to the external field is opposite to the one due to the external reserv…
We analyze the static response to perturbations of nonequilibrium steady states that can be modeled as one-dimensional diffusions on the circle. We demonstrate that an arbitrary perturbation can be broken up into a combination of three specific classes of perturbations that can be fruitfully addressed individually. For each class, we derive a simple formula that quantitatively characterizes the response in terms of the strength of nonequilibrium driving valid arbitrarily far from equilibrium.
In a recent paper [P. Strasberg and M. Esposito, Phys. Rev. E {\bf 101}, 050101(R) (2020)] an attempt is presented to formulate the nonequilibrium thermodynamics of an open system in terms of the Hamiltonian of mean force. The purpose of the present comment is to clarify severe restrictions of this approach and also to stress that recently noted ambiguities [P. Talkner and P. Hänggi, Phys. Rev. E {\bf 94}, 022143 (2016)] of fluctuating thermodynamic potentials cannot be removed in the suggested way.
We review theory of information thermodynamics which incorporates effects of measurement and feedback into nonequilibrium thermodynamics of a small system, and discuss how the second law of thermodynamics should be extended for such situations. We address the issue of the maximum work that can be extracted from the system in the presence of a feedback controller (Maxwell's demon) and provide a few illustrative examples. We also review a recent experiment that realized a Maxwell's demon based on a feedback-controlled ratchet.
We establish a general theory of feedback control on classical stochastic thermodynamic systems, and generalize nonequilibrium equalities such as the fluctuation theorem and the Jarzynski equality in the presence of feedback control with multiple measurements. Our results are generalizations of the previous relevant works to the situations with general measurements and multi-heat baths. The obtained equalities involve additional terms that characterize the information obtained by measurements or the efficacy of feedback control. A generalized Szilard engine and a feedback-controlled ratchet ar…
The second law of ordinary thermodynamics and the second law of steady state thermodynamics, as proposed by Oono and Paniconi, are investigated from the microscopic point of view for the open quantum system. Based on the H-theorem of Lindblad, we show that both second laws are consistent with the quantum dynamics generated by the completely positive map. In addition, microscopic expressions of entropy production and ``housekeeping heat'' are obtained for some classes of dynamical quantum systems.
We explore driven lattice gases for the existence of an intensive thermodynamic variable which could determine "equilibration" between two nonequilibrium steady-state systems kept in weak contact. In simulations, we find that these systems satisfy surprisingly simple thermodynamic laws, such as the zero-th law and the fluctuation-response relation between the particle-number fluctuation and the corresponding susceptibility remarkably well. However at higher densities, small but observable deviations from these laws occur due to nontrivial contact dynamics and the presence of long-range spatial…
We develop the stochastic approach to thermodynamics based on the stochastic dynamics, which can be discrete (master equation) continuous (Fokker-Planck equation), and on two assumptions concerning entropy. The first is the definition of entropy itself and the second, the definition of entropy production rate which is nonnegative and vanishes in thermodynamic equilibrium. Based on these assumptions we study interacting systems with many degrees of freedom in equilibrium or out of thermodynamic equilibrium, and how the macroscopic laws are derived from the stochastic dynamics. These studies inc…
We here present the complete analysis of experiments on driven Brownian motion and electric noise in a $RC$ circuit, showing that thermodynamic entropy production can be related to the breaking of time-reversal symmetry in the statistical description of these nonequilibrium systems. The symmetry breaking can be expressed in terms of dynamical entropies per unit time, one for the forward process and the other for the time-reversed process. These entropies per unit time characterize dynamical randomness, i.e., temporal disorder, in time series of the nonequilibrium fluctuations. Their difference…
The typicality of the canonical state shows that majority of the states are indistinguishable from equilibrium, and thus the nonequilibrium states are exceptionally rare in the extremely high-dimensional Hilbert space. On the contrary, we can easily apply an external force acting on the system, and then the actual density matrix quantitatively deviates from the canonical state specified by the system Hamiltonian at each instance. To express how the external forcing amounts to the deviation from equilibrium, we give a universal thermodynamic expression of the lower bound of Hilbert-Schmidt dist…
We propose a tensor-network algorithm for discrete-time stochastic dynamics of a homogeneous system in the thermodynamic limit. We map a $d$-dimensional nonequilibrium Markov process to a $(d+1)$-dimensional infinite tensor network by using a higher-order singular-value decomposition. As an application of the algorithm, we compute the nonequilibrium relaxation from a fully magnetized state to equilibrium of the one- and two- dimensional Ising models with periodic boundary conditions. Utilizing the translational invariance of the systems, we analyze the behavior in the thermodynamic limit direc…
A Unified Nonequilibrium Framework: Thermodynamic Distance, Dissipation, and Stationary Laws via Effective State Count, Variational Stationarity, and Thermodynamic Bounds
本文提出一个基于有效态计数的非平衡热力学变分框架，定义热力学距离并分解熵产生，导出涨落对称性与热力学界。
We show that a nominal temperature can be consistently and uniquely defined everywhere in the phase diagram of large classes of nonequilibrium kinetic Ising spin models. In addition, we confirm the recent proposal that, at critical points, the large-time ``fluctuation-dissipation ratio'' $X_\infty$ is a universal amplitude ratio and find in particular $X_\infty \approx 0.33(2)$ and $X_\infty = 1/2$ for the magnetization in, respectively, the two-dimensional Ising and voter universality classes.
Emergent Competition Between Dynamical Channels in Nonequilibrium Systems
本文提出一种无排斥的连续时间动力学蒙特卡洛框架，研究由多种并发动力学机制调控的随机系统。通过分析驱动反铁磁伊辛模型，发现不同动力学机制的共存能重塑非平衡相图，稳定反铁磁序。结果揭示了动力学通道共演化的关键作用。
We show that intensive thermodynamic parameters associated to additive conserved quantities can be naturally defined from a statistical approach in far-from-equilibrium steady-state systems, under few assumptions, and without any detailed balance requirement. It may apply, e.g., to dissipative systems like granular gases where volume or mass is still conserved, or to systems with periodic boundary conditions where fluxes of conserved quantities are present. We emphasize the usefulness of this concept to characterize the coexistence of different nonequilibrium phases, and discuss the influence …
Development of steady state thermodynamics and statistical mechanics depends crucially on our ability to develop notions of equilibrium thermodynamics for nonequilibrium steady states (NESS). The present paper considers the development of heat capacity. A modified definition is proposed which continues to maintain the same relation to steady state Shannon entropy as in equilibrium, thus providing a thermodynamically consistent treatment of NESS heat capacity.
We generalize an idea in the works of Landauer and Bennett on computations, and Hill's in chemical kinetics, to emphasize the importance of kinetic cycles in mesoscopic nonequilibrium thermodynamics (NET). For continuous stochastic systems, a NET in phase space is formulated in terms of cycle affinity $\nabla\wedge\big(\mathbf{D}^{-1}\mathbf{b}\big)$ and vorticity potential $\mathbf{A}(\mathbf{x})$ of the stationary flux $\mathbf{J}^{*}=\nabla\times\mathbf{A}$. Each bivectorial cycle couples two transport processes represented by vectors and gives rise to Onsager's reciprocality; the scalar pr…
Nonequilibrium Critical Dynamics with Emergent Supersymmetry
本文针对超对称性在非平衡动力学中的作用机制不明的问题，通过大规模量子蒙特卡洛模拟研究含涌现$\mathcal{N}=2$时空超对称性的量子临界点的Kibble-Zurek动力学，揭示了其有限时间标度规律及超对称性的体现，为相关实验探测提供理论指导。
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…
We extend Jarzynski's work relation and the second law of thermodynamics to a heat conducting system which is operated by an external agent. These extensions contain a new non equilibrium contribution expressed as the violation of the (linear) response relation caused by the operation. We find that a natural extension of the minimum work principle involves information about the time-reversed operation, and is far from straightforward. Our work relation may be tested experimentally especially when the temperature gradient is small.
We present an approach based on a density matrix expansion to study thermodynamic properties of a quantum system strongly coupled to two or more baths. For slow external driving of the system, we identify the adiabatic and nonadiabatic contributions to thermodynamic quantities, and we show how the first and second laws of thermodynamics are manifested in the strong coupling regime. Particularly, we show that the entropy production is positive up to second order in the driving speed. The formulation can be applied both for Bosonic and Fermionic systems, and recovers previous results for the equ…
Emergent universal statistics in nonequilibrium systems with dynamical scale selection
研究揭示了非平衡系统中通过长度尺度选择形成的普遍统计特性，提出了一种统一的非平衡统计场理论。
Using an additivity property, we study particle-number fluctuations in a system of interacting self-propelled particles, called active Brownian particles (ABPs), which consists of repulsive disks with random self-propulsion velocities. From a fluctuation-response relation - a direct consequence of additivity, we formulate a thermodynamic theory which captures the previously observed features of nonequilibrium phase transition in the ABPs from a homogeneous fluid phase to an inhomogeneous phase of coexisting gas and liquid. We substantiate the predictions of additivity by analytically calculati…
We use the work done on and the heat removed from a system to maintain it in a nonequilibrium steady state for a thermodynamic-like description of such a system as well as of its fluctuations. Based on a generalized Onsager-Machlup theory for nonequilibrium steady states we indicate two ambiguities, not present in an equilibrium state, in defining such work and heat: one due to a non-uniqueness of time-reversal procedures and another due to multiple possibilities to separate heat into work and an energy difference in nonequilibrium steady states. As a consequence, for such systems, the work an…
We consider a macroscopic system in contact with boundary reservoirs and/or under the action of an external field. We discuss the case in which the external forcing depends explicitly on time and drives the system from a nonequilibrium state to another one. In this case the amount of energy dissipated along the transformation becomes infinite when an unbounded time window is considered. Following the general proposal by Oono and Paniconi and using results of the macroscopic fluctuation theory, we give a natural definition of a renormalized work. We then discuss its thermodynamic relevance by s…
Topologically-constrained fluctuations and thermodynamics regulate nonequilibrium response
推导了由状态空间拓扑和热力学驱动强度决定的非平衡响应约束，且无需额外动力学信息，并在受体结合模型中揭示了化学驱动对Hill系数的增强作用。
Dissipative effects in electromagnetism on macroscopic scales are examined by coarse graining the microscopic Maxwell equations with respect to time. We illustrate a procedure to derive the dissipative effects on the macroscopic scale by using a Green-Kubo type expression in terms of the microscopic fluctuations and the correlations between them. The resulting macroscopic Maxwell equations are formulated within the General Equation for the Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) framework, accounting also for inhomogeneous temperature.
Among various possible routes to extend entropy and thermodynamics to nonequilibrium steady states (NESS), we take the one which is guided by operational thermodynamics and the Clausius relation. In our previous study, we derived the extended Clausius relation for NESS, where the heat in the original relation is replaced by its "renormalized" counterpart called the excess heat, and the Gibbs-Shannon expression for the entropy by a new symmetrized Gibbs-Shannon-like expression. Here we concentrate on Markov processes describing heat conducting systems, and develop a new method for deriving ther…
Thermodynamics is based on the notions of energy and entropy. While energy is the elementary quantity governing physical dynamics, entropy is the fundamental concept in information theory. In this work, starting from first principles, we give a detailed didactic account on the relations between energy and entropy and thus physics and information theory. We show that thermodynamic process inequalities, like the Second Law, are equivalent to the requirement that an effective description for physical dynamics is strongly relaxing. From the perspective of information theory, strongly relaxing dyna…
We show the link between U1 lattice gauge theories and the off-equilibrium thermodynamics of a large class of nonlinear oscillators networks. The coupling between the oscillators plays the role of a gauge field, or connection, on the network. The thermodynamical forces that drive energy flows are expressed in terms of the curvature of the connection, analogous to a geometric phase. The model, which holds both close and far from equilibrium, predicts the existence of persistent energy and particle currents circulating in close loops through the network. The predictions are confirmed by numerica…
We reconsider a well-known relationship between the fluctuation theorem and the second law of thermodynamics by evaluating a probability measure-valued process. In order to establish a bridge between microscopic and macroscopic behaviors, we consider the thermodynamic limit of a stochastic dynamical system following the fundamental procedure often used in statistical mechanics. The thermodynamic path characterizing a macroscopic dynamical behavior can be formulated as an infimum of the action functional for the probability measure-valued process. In our formulation, the second law of thermodyn…
We refute the criticism expressed in a comment by P. Talkner and P. Hänggi [Phys. Rev. E 102, 066101 (2020)] on our paper Phys. Rev. E 101, 050101(R) (2020). We first make clear that our paper is free of any technical mistakes. We then defend the statements of our manuscript which were claimed to be taken out of context. Finally, we give clear arguments showing that the basic concepts we rely on are meaningful and have a deep rational.
For macroscopic systems, the second law of thermodynamics establishes an inequality between the amount of work performed on a system in contact with a thermal reservoir, and the change in its free energy. For microscopic systems, this result must be considered statistically, as fluctuations around average behavior become substantial. In recent years it has become recognized that these fluctuations satisfy a number of strong and unexpected relations, which remain valid even when the system is driven far from equilibrium. We discuss these relations, and consider what they reveal about the second…
Controlling thermodynamic cycles to minimize the dissipated heat is a longstanding goal in thermodynamics, and more recently, a central challenge in stochastic thermodynamics for nanoscale systems. Here, we introduce a theoretical and computational framework for optimizing nonequilibrium control protocols that can transform a system between two distributions in a minimally dissipative fashion. These protocols optimally transport a system along paths through the space of probability distributions that minimize the dissipative cost of a transformation. Furthermore, we show that the thermodynamic…
We examine the Jarzynski equality for a quenching process across the critical point of second-order phase transitions, where absolute irreversibility and the effect of finite-sampling of the initial equilibrium distribution arise on an equal footing. We consider the Ising model as a prototypical example for spontaneous symmetry breaking and take into account the finite sampling issue by introducing a tolerance parameter. For a given tolerance parameter, the deviation from the Jarzynski equality depends onthe reduced coupling constant and the system size. In this work, we show that the deviatio…
A nonequilibrium thermodynamic theory demonstrating an induction effect of a statistical nature is presented. We have shown that this thermodynamic induction can arise in a class of systems that have variable kinetic coefficients (VKC). In particular if a kinetic coefficient associated with a given thermodynamic variable depends on another thermodynamic variable then we have derived an expression that can predict the extent of the induction. The amount of induction is shown to be proportional to the square of the driving force. The nature of the intervariable coupling for the induction effect …
We ask what happens when two systems having a nonequilibrium steady state are kept in contact and allowed to exchange a quantity, say mass, which is conserved in the combined system. Will the systems eventually evolve to a new stationary state where certain intensive thermodynamic variable, like equilibrium chemical potential, equalizes following zeroth law of thermodynamics and, if so, under what conditions is it possible? We argue that the zeroth law would hold, provided both systems have short-ranged spatial correlations and they {\it interact weakly} to exchange mass with rates satisfying …
We introduce axiomatically a complete thermodynamic formalism for a single macromolecule, either with or without detailed balance, in an isothermal ambient fluid based on its stochastic dynamics. With detailed balance, the novel theory yields mesoscopic, nonequilibrium generalizations for entropy and free energy of the macromolecule. Mesoscopic energy and entropy fluctuate. Expectation of entropy production equals zero if and only if the macromolecule is at thermal equilibrium, in which we show entropy still fluctuates but free energy is a constant. The entropy fluctuation a la L.D. Landau, pr…
Nonequilibrium equalities have attracted considerable interest in the context of statistical mechanics and information thermodynamics. What is remarkable about nonequilibrium equalities is that they apply to rather general nonequilibrium situations beyond the linear response regime. However, nonequilibrium equalities are known to be inapplicable to some important situations. In this thesis, we introduce a concept of absolute irreversibility as a new class of irreversibility that encompasses the entire range of those irreversible situations to which the conventional nonequilibrium equalities ar…
After the justification of the maximum entropy approach for equilibrium thermodynamic system, and of a maximum path entropy algorithm for nonequilibrium thermodynamic systems by virtue of the principle of virtual work, we present in this paper another application of the principle to thermodynamic systems out of equilibrium. Unlike the justification of maximum path entropy for the motion trajectories during a period of time, this work is on the maximum of the entropy defined as a measure of the momentary dynamical uncertainty as a function of the probability distribution over the microstates of…
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