Fluctuation theorem for quasi-integrable systems

Laboratoire de Physique Statistique, Département de physique de l'ENS, École Normale Supérieure, PSL Research University; Université Paris Diderot, Sorbonne Paris-Cité; Sorbonne Universités, UPMC Univ. Paris 06, CNRS - 24 rue Lhomond, 75005 Paris, France

Received: 25 September 2018
Accepted: 5 October 2018

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.