Fluctuation Theorem for Quasi-Integrable Systems

TL;DR

This paper establishes a Fluctuation Theorem applicable to isolated quasi-integrable systems, revealing how such systems approach equilibrium without external influence and providing insights into soliton dynamics.

Contribution

It introduces a novel Fluctuation Theorem for classical and quantum quasi-integrable systems, applicable regardless of system size or time scale, unlike traditional fluctuation relations.

Findings

FT describes probability ratios of soliton death and resurrection in Fermi-Pasta-Ulam chain

FT characterizes how quasi-integrable systems descend entropy landscapes

System always moves towards equilibrium but not necessarily along a gradient

Abstract

A Fluctuation Theorem (FT), both Classical and Quantum, describes the large-deviations in the approach to equilibrium of an isolated quasi-integrable system. Two characteristics make it unusual: (i) it concerns the internal dynamics of an isolated system without external drive, and (ii) unlike the usual FT, the system size, or the time, need not be small for the relation to be relevant, provided the system is close to integrability. As an example, in the Fermi-Pasta-Ulam chain, the relation gives information on the ratio of probability of death to resurrection of solitons. For a coarse-grained system the FT describes how the system `skis' down the (minus) entropy landscape: always descending but generically not along a gradient line.