Transient fluctuation theorem in closed quantum systems

TL;DR

This paper demonstrates that the entropy dynamics in closed quantum systems exhibit a transient fluctuation theorem and can be modeled as an Ornstein-Uhlenbeck process, supported by numerical and analytical evidence.

Contribution

It introduces a framework linking quantum entropy dynamics to fluctuation theorems and stochastic processes in pure state evolutions of closed quantum systems.

Findings

Entropy dynamics follow a transient fluctuation theorem.

Expectation values are modeled as Ornstein-Uhlenbeck processes.

Numerical and analytical results support the theoretical framework.

Abstract

Our point of departure are the unitary dynamics of closed quantum systems as generated from the Schr\"odinger equation. We focus on a class of quantum models that typically exhibit roughly exponential relaxation of some observable within this framework. Furthermore, we focus on pure state evolutions. An entropy in accord with Jaynes principle is defined on the basis of the quantum expectation value of the above observable. It is demonstrated that the resulting deterministic entropy dynamics are in a sense in accord with a transient fluctuation theorem. Moreover, we demonstrate that the dynamics of the expectation value are describable in terms of an Ornstein-Uhlenbeck process. These findings are demonstrated numerically and supported by analytical considerations based on quantum typicality.