Entropy Production and the Role of Correlations in Quantum Brownian Motion

TL;DR

This paper investigates quantum entropy production in the driven Caldeira-Leggett model, comparing different definitions, analyzing correlations, and studying entanglement dynamics to deepen understanding of quantum thermodynamics.

Contribution

It provides a detailed comparison of entropy production definitions, explores their decomposition into correlations, and examines quantum entanglement evolution in a solvable quantum Brownian motion model.

Findings

Different entropy production definitions show consistent qualitative behavior.

Correlations significantly contribute to entropy production at various couplings and temperatures.

Quantum entanglement between system and environment evolves dynamically, affecting thermodynamic properties.

Abstract

We perform a study on quantum entropy production, different kinds of correlations, and their interplay in the driven Caldeira-Leggett model of quantum Brownian motion. The model, taken with a large but finite number of bath modes, is exactly solvable, and the assumption of a Gaussian initial state leads to an efficient numerical simulation of all desired observables in a wide range of model parameters. Our study is composed of three main parts. We first compare two popular definitions of entropy production, namely the standard weak-coupling formulation originally proposed by Spohn and later on extended to the driven case by Deffner and Lutz, and the always-positive expression introduced by Esposito, Lindenberg and van den Broeck, which relies on the knowledge of the evolution of the bath. As a second study, we explore the decomposition of the Esposito et al. entropy production into system-environment and intra-environment correlations for different ranges of couplings and temperatures. Lastly, we examine the evolution of quantum correlations between the system and the environment, measuring entanglement through logarithmic negativity.