Quantum Crooks fluctuation theorem and quantum Jarzynski equality in the presence of a reservoir

TL;DR

This paper extends Crooks Fluctuation Theorem and Jarzynski Equality to open quantum systems, providing explicit work expressions and validating the theorems through numerical simulations beyond linear response.

Contribution

It introduces a quantum generalization of key fluctuation theorems for open systems, clarifies their relation to classical forms, and demonstrates their validity via numerical models.

Findings

Quantum Crooks Fluctuation Theorem and Jarzynski Equality are valid for open quantum systems.

Explicit microscopic work expressions are derived for arbitrary protocols.

Numerical simulations confirm the theorems beyond linear response regimes.

Abstract

We consider the quantum mechanical generalization of Crooks Fluctuation Theorem and Jarzynski Equality for an open quantum system. The explicit expression for microscopic work for an arbitrary prescribed protocol is obtained, and the relation between quantum Crooks Fluctuation Theorem, quantum Jarzynski Equality and their classical counterparts are clarified. Numerical simulations based on a two-level toy model are used to demonstrate the validity of the quantum version of the two theorems beyond linear response theory regime.