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.     

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.     

Non-equilibrium thermodynamics of interfacial systems

The theory of non-equilibrium thermodynamics is applied to a multi-component system containing an interface using a method developed by Bedeaux, Albano, and Mazur. A singular mass density is allowed at the interface as well as singular densities of energy and entropy. All currents are also allowed to be singular at the interface. The conservation laws and the Gibbs relation for the entropy are used to derive the entropy production at the surface. Linear laws relating the fluxes and thermodynamic forces are presented. The theory is then applied to a two component system where one of the phases is a liquid and the other a low density gas and the boundary conditions at the free surface of the liquid derived. The boundary conditions include the conditions used by Levich in his theory of the damping of waves by surface-active substances, but include other effects as well.     

Macroscopic aspects of mixing distance in nonequilibrium thermodynamics

In this paper, we describe several further developments in the application of the principle of increasing mixing character, and the related principle of decreasing mixing distance, to the time-dependent behavior of macroscopic systems. There are three main parts to this paper. In the first, some basic assumptions are discussed which are sufficient for the validity of the principle of decreasing mixing distance, and the macroscopic formulation thereof. It is shown that the principle holds, not only for a system in contact with a heat bath, but also in linear thermodynamics for open systems with time-independent boundary conditions, and with nonequilibrium steady-state, rather than equilibrium, solutions. In the second part, a new proof is given for a result previously obtained by one of us which permits the formulation of the principle in terms of observable thermodynamic properties of macroscopic systems. The new proof is more general than the old, in that one of the assumptions used before has been dropped. Finally, several simple examples are discussed, which show clearly how this principle directly yields more detailed information about the time evolution of a system than is afforded by traditional thermodynamics.     

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.     

A stochastic approach to nonequilibrium thermodynamics of chemical reaction system

Nonequilibrium thermodynamics is formulated by combining the nonlinear Fokker-Planck equation with the so-called Gibbs entropy postulate. The entropy production thus derived consists of two parts: one is of the same form as the usual entropy production and the other is the fluctuating part attendant on it. The evolution criterion can easily be verified in the stochastic framework. For illustration the system governed by the linear Fokker-Planck equation is in detail discussed.     

Quantum thermodynamics of nonequilibrium. Onsager reciprocity and dispersion-dissipation relations

A generalized Onsager reciprocity theorem emerges as an exact consequence of the structure of the nonlinear equation of motion of quantum thermodynamics and is valid for all the dissipative nonequilibrium states, close and far from stable thermodynamic equilibrium, of an isolated system composed of a single constituent of matter with a finite-dimensional Hilbert space. In addition, a dispersion-dissipation theorem results in a precise relation between the generalized dissipative conductivity that describes the mutual interrelation between dissipative rates of a pair of observables and the codispersions of the same observables and the generators of the motion. These results are presented together with a review of quantum thermodynamic postulates and general results.     

Conserved moments in nonequilibrium field dynamics

We demonstrate with the example of Cahn-Hilliard dynamics that the macroscopic kinetics of first-order phase transitions exhibits an infinite number of constants of motion. Moreover, this result holds in any space dimension for a broad class of nonequilibrium processes whose macroscopic behavior is governed by equations of the form /t = W(), where is an order parameter,W is an arbitrary function of , and is a linear Hermitian operator. We speculate on the implications of this result.     

Nonlinear and nonequilibrium dynamics in geomaterials

The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a simple macroscopic dynamical model. At even higher strains, effects due to a driven nonequilibrium state, and relaxation from it, complicate the characterization of the nonlinear behavior.     

Modeling laser-assisted particle removal using molecular dynamics

Laser-assisted particle removal, a method of cleaning nano- to micro-scale particles from surfaces, was modeled using molecular dynamics. A two-dimensional molecular model consisting of substrate, particle, and adsorbed fluid was used. In order to obtain statistical accuracy of cleaning efficiencies, over 1200 particle-removal simulations were conducted. The effects of fluid thickness and substrate temperature were both considered, and good qualitative agreement with experimental results was obtained. The molecular dynamics approach is shown to be an effective way to study these systems. PACS 81.65.Cf; 79.20.Ds     

Thermal mechanics: A quantum mechanical analogue of nonequilibrium statistical thermodynamics

A formal but not conventional equivalence between stochastic processes in nonequilibrium statistical thermodynamics and Schrödinger dynamics in quantum mechanics is shown. It is found, for each stochastic process described by a stochastic differential equation of Itô type, there exists a Schrödinger-like dynamics in which the absolute square of a wavefunction gives us the same probability distribution as the original stochastic process. In utilizing this equivalence between them, that is, rewriting the stochastic differential equation by an equivalent Schrödinger equation, it is possible to obtain the notion of deterministic limit of the stochastic process as a semi-classical limit of the “Schrödinger” equation. The deterministic limit thus obtained improves the conventional deterministic approximation in the sense of Onsager-Machlup. The present approach is valid for a general class of stochastic equations where local drifts and diffusion coefficients depend on the position. Two concrete examples are given. It should be noticed that the approach in the present form has nothing to do with the conventional one where only a formal similarity between the Fokker-Planck equation and the Schrödinger equation is considered.     

The method of moments and the nonequilibrium thermodynamics of rarefied gases

A generalized variant of the nonequilibrium thermodynamics of rarefied gases based on the linearized equations of Grad’s method of moments is studied. It is shown that despite the more complicated form of the thermodynamic forces, which include spatial derivatives of the fluxes, entropy production remains a bilinear combination of generalized thermodynamic fluxes and forces. Using perturbation theory in the small Knudsen number, the expressions obtained can be reduced to the well-known results of the Chapman-Enskog method at the level of the linearized Burnett approximation. Zh. éksp. Teor. Fiz. 113, 2081–2095 (June 1998)