Heat exchange and fluctuation in Gaussian thermal states in the quantum realm

TL;DR

This paper extends the exchange fluctuation theorem to quantum Gaussian states in thermal equilibrium using Wigner functions, showing it converges to classical results as Planck's constant approaches zero.

Contribution

It introduces a quantum version of the exchange fluctuation theorem for Gaussian states using phase-space formalism, bridging quantum and classical thermodynamics.

Findings

Quantum fluctuation theorem matches classical results in the classical limit.

Wigner function formalism effectively describes heat exchange in quantum states.

The theorem applies to Gaussian states in thermal equilibrium at different temperatures.

Abstract

The celebrated exchange fluctuation theorem -- proposed by Jarzynski and W\'ozcik, (Phys Rev. Lett. 92, 230602 (2004)) for heat exchange between two systems in thermal equilibrium at different temperatures -- is explored here for quantum Gaussian states in thermal equilibrium. We employ Wigner distribution function formalism for quantum states, which exhibits close resemblance with the classcial phase-space trajectory description, to arrive at this theorem. For two Gaussian states in thermal equilibrium at two different temperatures kept in contact with each other for a fixed duration of time we show that the quantum Jarzyinski-W\'ozcik theorem agrees with the corresponding classical result in the limit \hbar->0.