Differential relations of the nonlocal nonequilibrium thermodynamics of martensitic transformations

Differential relations describing the change in the degree of martensitic transformation with change in the external temperature and pressure are derived. As an illustration, the relations are applied to the analysis of the experimental situation of apparent violation of the Clausing-Clapeyron equation.     

Chaotic hypothesis: Onsager reciprocity and fluctuation-dissipation theorem

It is shown that the chaoticity hypothesis recently introduced in statistical mechanics, which is analogous to Ruelle's principle for turbulence, implies the Onsager reciprocity and the fluctuation-dissipation theorem in various reversible models for coexisting transport phenomena.This paper is dedicated to David Ruelle on the occasion of his 60th birthday.     

Nonlinear fluctuation-dissipation relations and stochastic models in nonequilibrium thermodynamics: I. Generalized fluctuation-dissipation theorem

The paper is devoted to the theory of thermal fluctuations in nonlinear macroscopic systems and to the derivation of variational principles of nonlinear nonequilibrium thermodynamics. In the first part of the paper rigorous universal fluctuation-dissipation relations for nonlinear classical and quantum systems, subjected to dynamic as well as thermodynamic perturbations, are derived and analyzed. General expressions for dissipative fluxes and nonlinear transfer coefficients with the help of fluctuation cumulants are found. The canonical structure of nonlinear evolution equations of macrovariables is derived and the rule of introducing langevinian random forces into these equations, in accordance with fluctuation-dissipation relations. A Markovian theory of fluctuations in a stationary nonequilibrium state is constructed.     

Mutual (isothermal) diffusion in binary hard-sphere mixtures: The effects of the Onsager reciprocity relations

The mutual diffusion coefficients of the Revised Enskog Theory of van Beijeren and Ernst and the Standard Theory of Thorne are compared. The former theory is consistent with the Onsager Reciprocity Relations while the latter is not. The diffusion constant of the Revised Theory is found to be as much as 30% larger than that predicted by the Standard Theory.     

Relationship between the thermodynamics of nonequilibrium state and the thermodynamics of nonequilibrium processes

The concept and equations of the thermodynamics of nonequilibrium state are compared with the postulates of linear thermodynamics of nonequilibrium processes. It is shown that all the four basic postulates can be obtained as consequences of the equations of the thermodynamics of nonequilibrium state. In the limiting case of small deviations from equilibrium, the thermodynamics of nonequilibrium state are reduced to linear thermodynamics of nonequilibrium processes.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 10–14, December, 1990.     

Theory of quantum fluctuations and the Onsager relations

A microscopic model is constructed within the theory of normal fluctuations for quantum systems, yielding an irreversible dynamics satisfying the Onsager relations. The property of return to equilibrium and the principle of minimal entropy production are proved.     

The Onsager reciprocity relation and generalized efficiency of a thermal Brownian motor

Based on a general model of Brownian motors, the Onsager coefficients and generalized efficiency of a thermal Brownian motor are calculated analytically. It is found that the Onsager reciprocity relation holds and the Onsager coefficients are not affected by the kinetic energy change due to the particle's motion. Only when the heat leak in the system is negligible can the determinant of the Onsager matrix vanish. Moreover, the influence of the main parameters characterizing the model on the generalized efficiency of the Brownian motor is discussed in detail. The characteristic curves of the generalized efficiency varying with these parameters are presented, and the maximum generalized efficiency and the corresponding optimum parameters are determined. The results obtained here are of general significance. They are used to analyze the performance characteristics of the Brownian motors operating in the three interesting cases with zero heat leak, zero average drift velocity or a linear response relation, so that some important conclusions in current references are directly included in some limit cases of the present paper.     

颗粒介质的结构及热力学

颗粒介质具有远程无序和近程有序的结构, 是产生动力学不均匀性(dynamical heterogeneity) 和复杂不可逆过程的根源. 本文分析了颗粒介质的结构特征、变形和能量耗散之间的内在关联, 讨论了颗粒介质的弹性, 提出了流变应变增量、耦合应变增量和弹性应变增量的应变增量分解方式. 沿用非平衡热力学框架, 引入表征运动无序的动理学颗粒温度T^k和表征弹性应力涨落的构型温度T^c, 作为非平衡态变量, 建立了双颗粒温度热力学(two-granular-temperature thermodynamics, TGT理论), 注重分析了不可逆过程中的热力学力和流, 并与著名的砂土内变量热力学进行了对比.     

铁电分子场与Onsager关系

在考虑体系内部相互作用非均匀性的基础上,从不可逆过程热力学的角度,在铁电领域重新引入“分子场”的概念,并给出了“分子场”所满足的热力学方程及物性方程.对铁电相变中的局域性质作了深入探讨 关键词： 分子场 局域性 铁电相变     

Electron-ion interference and Onsager reciprocity in mixed ionic-electronic transport in TiO2

Onsager's reciprocity theorem has been extensively discussed for fluid systems and its validity generally accepted. The application of the theorem to solid state, however, is not always transparent due to additional complications that have no counterparts in fluids, and its validity has not been so exhaustively examined experimentally either. Here we show that in the phenomenon of mixed ionic-electronic conduction in TiO2 (rutile), the theorem is verified experimentally, and the Onsager cross coefficient can be even larger than a direct one, contrary to the conventional belief.     

Onsager relations for transport in inhomogeneous media

The nonlinear equations that describe transport in inhomogeneous media cannot be obtained by a straightforward extension of the known phenomenological equations for homogeneous media. One cannot therefore asserta priori that the Onsager reciprocity relations remain valid. Previously the correct equations have been obtained for three special models using kinetic theory. It is here shown that in these models the Onsager relations do indeed hold, provided that they are formulated with care.     

Rayleigh reciprocity relations:Applications

Classical reciprocity relations have wide applications in acoustics, from field representation to generalized optical theorem. In this paper we introduce our recent results on the applications and generalization of classical Rayleigh reciprocity relation: higher derivative reciprocity relations as a generalization of the classical one and a theoretical proof on the Green's function retrieval from volume noises.     

Nonlinear fluctuation-dissipation relations and stochastic models in nonequilibrium thermodynamics: II. Kinetic potential and variational principles for nonlinear irreversible processes

On the basis of a complete system of fluctuation-dissipation relations, considered in the first part of this series, a variational principle for nonlinear irreversible processes is derived. According to this principle the virtual entropy production functional (analogous to the action in mechanics) has an absolute minimum meaning on the real trajectory of a system. The universal structure of the “kinetic potential” and the “lagrangian” of a system, each contain complete information about fluctuations of macrovariables. The connection of the lagrangian with the markovian kinetic operator of macrovariables is stated. Fundamental properties of dissipative potentials, reflecting microscopic reversibility, are considered. The derived variational principle can be applied to closed systems (the steady state of which is equilibrium) as well as to open ones (when external dynamic forces cause entropy flux through the system and put it into a steady non-equilibrium state). Canonical transformations of macrovariables are considered.     

Modeling interfacial dynamics using nonequilibrium thermodynamics frameworks

In recent years several nonequilibrium thermodynamic frameworks have been developed capable of describing the dynamics of multiphase systems with complex microstructured interfaces. In this paper we present an overview of these frameworks. We will discuss interfacial dynamics in the context of the classical irreversible thermodynamics, extended irreversible thermodynamics, extended rational thermodynamics, and GENERIC framework, and compare the advantages and disadvantages of these frameworks.     

Higher Order Quantum Onsager Coefficients from Dynamical Invariants

Functionals representing dynamical invariants under unitary quantum dynamics of open systems are used to derive Onsager coefficients for entropy production in irreversible processes if the nonunitary time evolution is determined by quantum dynamical semigroups. The procedure allows a derivation from first principles of the quantum analogue to the classical case.