Nonequilibrium Work Relation from Schroedinger's Unrecognized Probability Theory

TL;DR

This paper reinterprets Jarzynski's nonequilibrium work relation through a novel reciprocal process framework based on Schroedinger's probability theory, revealing underlying symmetries and unifying various stochastic dynamics.

Contribution

It introduces a reciprocal process with real wave functions to derive the Jarzynski relation, connecting classical probability with hidden symmetries in nonequilibrium thermodynamics.

Findings

Jarzynski relation derived from reciprocal symmetry

Standard Markov processes are equivalent to reciprocal processes

Unified description for Fokker-Planck, Kramers, and relativistic Kramers equations

Abstract

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.