Entropy in Nonequilibrium Statistical Mechanics
| dc.creator | Kita, Takafumi | |
| dc.date | 2006-11-10 | |
| dc.date | 2007-06-03 | |
| dc.date.accessioned | 2026-07-07T08:05:39Z | |
| dc.date.available | 2026-07-07T08:05:39Z | |
| dc.description | 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 $H$-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. | |
| dc.description | 20 pages, 5 figures; addendum included in the revised version | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0611270 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0611270 | |
| dc.identifier | J. Phys. Soc. Jpn. 75, 114005 (2006); J. Phys. Soc. Jpn. 76, 067001 (2007) | |
| dc.identifier | doi:10.1143/JPSJ.75.114005; 10.1143/JPSJ.76.067001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130348 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Entropy in Nonequilibrium Statistical Mechanics | |
| dc.type | text |