Stiffness of Probability Distributions of Work and Jarzynski Relation for Non-Gibbsian Initial States

TL;DR

This paper explores how the probability distributions of work in driven quantum systems with non-Gibbsian initial states exhibit a form of stiffness, supporting the Jarzynski relation, with numerical evidence from spin systems and theoretical insights from Fermi's Golden Rule.

Contribution

It demonstrates that the work distribution stiffness leads to the Jarzynski relation's validity for a broad class of non-Gibbsian initial states in quantum systems.

Findings

Work distributions are largely independent of initial energies in studied systems.

The Jarzynski relation holds for non-Gibbsian initial states under certain conditions.

Numerical analysis confirms the assumption across integrable and non-integrable spin models.

Abstract

We consider closed quantum systems (into which baths may be integrated) that are driven, i.e., subject to time-dependent Hamiltonians. Our point of departure is the assumption that, if systems start in microcanonical states at some initial energies, the resulting probability distributions of work may be largely independent of the specific initial energies. It is demonstrated that this assumption has some far-reaching consequences, e.g., it implies the validity of the Jarzynski relation for a large class of non-Gibbsian initial states. By performing numerical analysis on integrable and non-integrable spin systems, we find the above assumption fulfilled for all considered examples. Through an analysis based on Fermi's Golden Rule, we partially relate these findings to the applicability of the eigenstate thermalization ansatz to the respective driving operators.