Entropy production of a quantum system in non-equilibrium environment: The effect of coherence

In this work, we study the entropy production of a quantum system undergoing dissipation in a non-equilibrium environment with weak coherence. We show that the entropy production rate can be decomposed into three contributions that are related to the system’s population, the system’s coherence, and the environmental coherence. With a specific model, we demonstrate that the initial coherence of the environment always contributes positively to the entropy production rate when the system is initially prepared in the thermal state. Nevertheless, the components of the entropy production rate exhibit distinct dependence on environmental coherence and may take negative values in certain ranges. Additionally, we show that when both the system and the environment are initially in states with finite nonzero coherence, the phase difference therein can reduce the entropy production rate to a level below that observed in a purely thermal environment. The stochastic versions of entropy production rate and its decomposition forms are also established from the perspective of quantum trajectories. Our findings on entropy production in the non-equilibrium environment provide beneficial supplement to conventional research in the thermal environment and are helpful for the development of high-performance thermal quantum technologies.