Entropy Production and the Role of Correlations in Quantum Brownian Motion

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.