Entropy Production in Quantum Brownian Motion

TL;DR

This paper explores how to coherently define and compare entropy production in quantum Brownian motion, revealing differences between two approaches and analyzing their behavior across various limits and conditions.

Contribution

It introduces and compares a new 'Poised' entropy production definition with an existing one, analyzing their differences and classical limits in quantum Brownian motion.

Findings

Both definitions yield positive entropy production and coincide at zero coupling.

The difference between the two definitions is always positive and grows with coupling strength.

In the classical limit, the 'Poised' entropy production matches stochastic thermodynamics results.

Abstract

We investigate how to coherently define entropy production for a process of transient relaxation in the Quantum Brownian Motion model for harmonic potential. We compare a form, called "Poised" (P), which after non-Markovian transients corresponds to a definition of heat as the change in the system Hamiltonian of mean force, with a recent proposal by Esposito (ELB) based on a definition of heat as the energy change in the bath. Both expressions yield a positive-defined entropy production and coincide for vanishing coupling strength, but their difference is proved to be always positive (after non-Markovian transients disappear) and to grow as the coupling strength increases. In the classical over-damped limit the "Poised" entropy production converges to the entropy production used in stochastic thermodynamics. We also investigate the effects of the system size, and of the ensuing Poincar\'e recurrences, and how the classical limit is approached. We close by discussing the strong-coupling limit, in which the ideal canonical equilibrium of the bath is violated.