Entropy in Nonequilibrium Statistical Mechanics
摘要
Entropy in nonequilibrium statistical mechanics is investigated theoretically so as to extend the well-established equilibrium framework to open nonequilibrium systems. We first derive a microscopic expression of nonequilibrium entropy for an assembly of identical bosons/fermions interacting via a two-body potential. This is performed by starting from the Dyson equation on the Keldysh contour and following closely the procedure of Ivanov, Knoll and Voskresensky [Nucl. Phys. A {\bf 672} (2000) 313]. The obtained expression is identical in form with an exact expression of equilibrium entropy and obeys an equation of motion which satisfies the -theorem in a limiting case. Thus, entropy can be defined unambiguously in nonequilibrium systems so as to embrace equilibrium statistical mechanics. This expression, however, differs from the one obtained by Ivanov {\em et al}., and we show explicitly that their ``memory corrections'' are not necessary. Based on our expression of nonequilibrium entropy, we then propose the following principle of maximum entropy for nonequilibrium steady states: ``The state which is realized most probably among possible steady states without time evolution is the one that makes entropy maximum as a function of mechanical variables, such as the total particle number, energy, momentum, energy flux, etc.'' During the course of the study, we also develop a compact real-time perturbation expansion in terms of the matrix Keldysh Green's function.
引用
@article{arxiv.cond-mat/0611270,
title = {Entropy in Nonequilibrium Statistical Mechanics},
author = {Takafumi Kita},
journal= {arXiv preprint arXiv:cond-mat/0611270},
year = {2007}
}
备注
20 pages, 5 figures; addendum included in the revised version