Quantum corrections to the entropy in a driven quantum Brownian motion model

TL;DR

This paper investigates quantum corrections to entropy in a driven quantum Brownian motion model by solving the quantum Langevin equation, providing analytical expressions for entropy evolution and corrections in different regimes, enhancing understanding of open quantum systems.

Contribution

It presents explicit quantum corrections to entropy and entropy production rates in quantum Brownian motion, extending classical thermodynamics to quantum regimes.

Findings

Analytical expression for the time evolution of the Wigner function.

Explicit quantum corrections to entropy for initial states with classical counterparts.

Quantum corrections to entropy production and heat dissipation rates.

Abstract

Quantum Brownian motion model is a typical model in the study of nonequilibrium quantum thermodynamics. Entropy is one of the most fundamental physical concepts in thermodynamics. In this work, by solving the quantum Langevin equation, we study the von Neumann entropy of a particle undergoing quantum Brownian motion. In both the strong and the weak coupling regimes, we obtain the analytical expression of the time evolution of the Wigner function in terms of the initial Wigner function. The result is applied to the thermodynamic equilibrium initial state, which reproduces its classical counterpart in the high-temperature limit. Based on these results, for those initial states having well-defined classical counterparts, we obtain the explicit expression of the quantum corrections to the entropy of the system. Moreover, under the Markovian approximation, we obtain the expression of the quantum corrections to the total entropy production rate ${e_{\rm p}}$ and the heat dissipation rate ${h_{\rm d}}$. Our results bring important insights to the understanding of entropy in open quantum systems.