Entropy production in quantum Brownian motion

We investigate how to coherently define entropy production for a process of transient relaxation in the quantum Brownian motion model for the harmonic potential. We compare a form, referred to as ‘poised’ (P), which after non-Markovian transients corresponds to a definition of heat as the change in the system Hamiltonian of mean force, with a recent proposal by Esposito et al (ELB) based on a definition of heat as the energy change in the bath. Both expressions yield a positive-definite entropy production and they coincide for vanishing coupling strength, but their difference is proved to be always positive (after non-Markovian transients disappear) and to grow as the coupling strength increases. In the classical ver-damped limit the ‘poised’ entropy production converges to the entropy production used in stochastic thermodynamics. We also investigate the effects of the system size, and of the ensuing Poincar´e recurrences, and how the classical limit is approached. We close by discussing the strongcoupling limit, in which the ideal canonical equilibrium of the bath is violated.