Theory of Transport Processes and the Method of the Nonequilibrium Statistical Operator

Abstract

The aim of this paper is to provide better understanding of a few approaches that have been proposed for treating nonequilibrium (time-dependent) processes in statistical mechanics with the emphasis on the interrelation between theories. The ensemble method, as it was formulated by Gibbs, has great generality and broad applicability to equilibrium statistical mechanics. Different macroscopic environmental constraints lead to different types of ensembles, with particular statistical characteristics. In the present work, the statistical theory of nonequilibrium processes which is based on nonequilibrium ensemble formalism is discussed. We also outline the reasoning leading to some other useful approaches to the description of the irreversible processes. The kinetic approach to dynamic many-body problems, which is important from the point of view of the fundamental theory of irreversibility, is alluded to. Appropriate references are made to papers dealing with similar problems arising in other fields. The emphasis is on the method of the nonequilibrium statistical operator (NSO) developed by Zubarev. The NSO method permits one to generalize the Gibbs ensemble method to the nonequilibrium case and to construct a nonequilibrium statistical operator which enables one to obtain the transport equations and calculate the transport coefficients in terms of correlation functions, and which, in the case of equilibrium, goes over to the Gibbs distribution. Although some space is devoted to the formal structure of the NSO method, the emphasis is on its utility. Applications to specific problems such as the generalized transport and kinetic equations, and a few examples of the relaxation and dissipative processes, which manifest the operational ability of the method, are considered.

Two-Temperature Model of Nonequilibrium Electron Relaxation: A Review

“…The theory of thermal relaxation of electrons in metals was further extended by P. B. Allen 14 . It has been proposed that TTM can be derived from D. N. Zubarev's non-equilibrium statistical operator (NSO) method 15,16 by systematic approximations, with this, one can obtain even more advanced results than TTM including the non-Markovian effects 17 . NSO method is based on a generalization of Gibbs' method of equilibrium states to non-equilibrium states.…”

Dynamics of a Bose-Einstein condensate of excited magnons

“…The formalism introduces the fundamental properties of historicity and irreversibility in the evolution of the nonequilibrium system where dissipative and pumping processes are under way. In terms of the dynamics generated by this full Hamiltonian the equations of evolution of the macroscopic state of the system are obtained in the framework of the NESEF-based nonlinear quantum kinetic theory [31,32,33,34,35,36,40,41,42,43]. We call the attention to the fact that the evolution equations are the quantum mechanical equations of motion averaged over the nonequilibrium ensemble, with the NESEF-kinetic theory providing a practical way of calculation.…”

Quasiaverages, symmetry breaking and irreducible Green functions method

“…The difference between P and M can be regarded as two different solutions of two integral equations (18) and (21). However, from the Dyson equation (21) only the full GF is seen to be expressed as a formal solution of the form…”

“…Equation (22) can be regarded as an alternative form of the Dyson equation (21) and the definition of M provides that the generalized mean-field GF G 0 is specified. On the contrary, for the scattering operator P , instead of the property…”