2017/09/30 by T. Koide · 1 citation
Physics and Astronomy · Mathematics · #cond-mat.stat-mech #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/2399-6528/aaa956
8 pages, no figure. Typos are corrected, and discussions and references are added. Accepted for publication in J. Phys. Commu
arxiv created 2018/01/17 · arxiv updated 2018/02/09
Jarzynski's nonequilibrium work relation can be understood as the realization of the (hidden) time-generator reciprocal symmetry satisfied for the conditional probability function. To show this, we introduce the reciprocal process where the classical probability theory is expressed with real wave functions, and derive a mathematical relation using the symmetry. We further discuss that the descriptions by the standard Markov process from an initial equilibrium state are indistinguishable from those by the reciprocal process. Then the Jarzynski relation is obtained from the mathematical relation for the Markov processes described by the Fokker-Planck, Kramers and relativistic Kramers equations.