Integral Fluctuation Theorem for Microcanonical and Pure States

TL;DR

This paper derives an integral fluctuation theorem for isolated quantum systems, specifically microcanonical and pure states, based on natural assumptions, and verifies it numerically in example systems.

Contribution

It introduces a derivation of the IFT for isolated quantum states using assumptions of stiffness and smoothness, extending fluctuation theorems to new quantum regimes.

Findings

IFT holds for microcanonical and pure states under assumptions

Numerical validation confirms the theorem and assumptions in example systems

Comparable results found by other researchers

Abstract

We present a derivation of the integral fluctuation theorem (IFT) for isolated quantum systems based on some natural assumptions on transition probabilities. Under these assumptions of "stiffness" and "smoothness" the IFT immediately follows for microcanonical and pure quantum states. We numerically check the IFT as well as the validity of our assumptions by analyzing two exemplary systems. We have been informed by T. Sagawa et al. that he and his co-workers found comparable numerical results and are preparing a corresponding paper, which should be available on the same day as the present text. We recommend reading their submission.