Nonequilibrium work relation from Schrödinger’s unrecognized probability theory
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چکیده
Jarzynski’s nonequilibriumwork relation can be understood as the realization of the (hidden) timegenerator reciprocal symmetry satisfied for the conditional probability function. To show this, we introduce the reciprocal process where the classical probability theory is expressedwith real wave functions, and derive amathematical relation using the symmetry.We further discuss that the descriptions by the standardMarkov process from an initial equilibrium state are indistinguishable from those by the reciprocal process. Then the Jarzynski relation is obtained from themathematical relation for theMarkov processes described by the Fokker–Planck, Kramers and relativistic Kramers equations.
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