Quantum-classical correspondence principle for heat distribution in quantum Brownian motion

TL;DR

This paper investigates the heat distribution in quantum Brownian motion using phase-space methods, demonstrating a quantum-classical correspondence and validating the quantum fluctuating heat concept through analytical results and fluctuation theorems.

Contribution

It provides an analytical expression for the heat characteristic function at any relaxation time and shows its classical limit, establishing a quantum-classical correspondence for heat distribution.

Findings

Heat distribution approaches classical results in the classical limit.

Fluctuating heat satisfies the exchange fluctuation theorem.

Long-time behavior shows complete thermalization.

Abstract

Quantum Brownian motion, described by the Caldeira-Leggett model, brings insights to understand phenomena and essence of quantum thermodynamics, especially the quantum work and heat associated with their classical counterparts. By employing the phase-space formulation approach, we study the heat distribution of a relaxation process in the quantum Brownian motion model. The analytical result of the characteristic function of heat is obtained at any relaxation time with an arbitrary friction coefficient. By taking the classical limit, such a result approaches the heat distribution of the classical Brownian motion described by the Langevin equation, indicating the quantum-classical correspondence principle for heat distribution. We also demonstrate that the fluctuating heat at any relaxation time satisfies the exchange fluctuation theorem of heat, and its long-time limit reflects complete thermalization of the system. Our research brings justification for the definition of the quantum fluctuating heat via two-point measurements.