von Neumann entropy and the entropy production of a damped harmonic oscillator

Abstract

In this paper we analyze the entropy and entropy production of a non-isolated quantum system described within the quantum Brownian motion framework. This is a very general and paradigmatic framework for describing non-isolated quantum systems and can be used in any kind of coupling regime. We start by considering the application of von Neumann entropy to an arbitrarily damped quantum system making use of its reduced density operator. We argue that this application is formally valid and develop a path integral method to evaluate that quantity analytically. We apply this technique to a harmonic oscillator in contact with a heat bath and obtain an exact form for its entropy. Then we study the entropy production of this system and enlighten important characteristics of its thermodynamical behavior on the pure quantum realm and also address their transition to the classical limit.

arXiv commentMain text: 7 pages, 2 figures. Supplementary material: 5 pages

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• Real-time methods for spectral functions
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• Quantum corrections to the entropy in a driven quantum Brownian motion model
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• Reconciling nonlinear dissipation with the bilinear model of two Brownian particles
• Over forty years of research towards the understanding of Quantum Brownian Motion -- the contributions of A. O. Caldeira
• Identical damped harmonic oscillators described by coherent states