Thermodynamics as a nonequilibrium path integral

TL;DR

This paper introduces a novel framework that uses a path integral approach and the work theorem to derive equilibrium distributions from non-equilibrium processes, even in interacting systems.

Contribution

It develops a method to construct an equilibrium distribution from non-equilibrium noise data using a special matrix derived from the work theorem.

Findings

The principal eigenvector of matrix ${ mf S}$ yields the equilibrium distribution.

The method applies to interacting systems without requiring equilibrium conditions.

It bridges the gap between non-equilibrium noise and equilibrium thermodynamics.

Abstract

Thermodynamics is a well developed tool to study systems in equilibrium but no such general framework is available for non-equilibrium processes. Only hope for a quantitative description is to fall back upon the equilibrium language as often done in biology. This gap is bridged by the work theorem. By using this theorem we show that the Barkhausen-type non-equilibrium noise in a process, repeated many times, can be combined to construct a special matrix ${\cal S}$ whose principal eigenvector provides the equilibrium distribution. For an interacting system ${\cal S}$, and hence the equilibrium distribution, can be obtained from the free case without any requirement of equilibrium.