Fluctuation theorems for quantum master equations

TL;DR

This paper derives quantum fluctuation theorems for driven quantum systems interacting with environments, using quantum master equations, and introduces quantum trajectories with entropy, heat, and work concepts.

Contribution

It presents a novel derivation of quantum fluctuation theorems based solely on quantum master equations, connecting quantum trajectories with thermodynamic quantities.

Findings

Derivation of a quantum fluctuation theorem for driven systems

Establishment of quantum integral fluctuation theorem and Jarzynski relation

Introduction of quantum trajectories and entropy in the context of QMEs

Abstract

A quantum fluctuation theorem for a driven quantum subsystem interacting with its environment is derived based solely on the assumption that its reduced density matrix obeys a closed evolution equation i.e. a quantum master equation (QME). Quantum trajectories and their associated entropy, heat and work appear naturally by transforming the QME to a time dependent Liouville space basis that diagonalizes the instantaneous reduced density matrix of the subsystem. A quantum integral fluctuation theorem, a steady state fluctuation theorem and the Jarzynski relation are derived in a similar way as for classical stochastic dynamics.