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

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.