Features of quantum thermodynamics induced by common environments based on collision model

Abstract

The common reservoir can cause some unique effects, such as dark state and steady-state coherence, which are extensively studied in the dynamics of open quantum system. In this work, by means of collision model, we explore features of quantum thermodynamics induced by common reservoirs. We first construct general formulations of thermodynamic quantities for the system consisting of N coupling subsystems embedded in M common thermal reservoirs. We confirm the existence of nonlocal work due to simultaneous interactions of subsystems with the common reservoirs resembling what is found for nonlocal heat. With a system of two coupled qubits in a common reservoir, we show that steady-state currents could emerge even when interactions of individual subsystems and the reservoir fulfill strict energy conservation. We also exhibit the effect of dark state on the steady-state currents. We then examine relations between the work cost, the system’s nonequilibrium steady-state and the extractable work. In particular, we find that in the presence of dark state, the work cost is only related to the coherence generated in the dynamical evolution but not to the one contributed by the initial dark state of the system. We also show the possible transformation of coherence into useful work in terms of ergotropy. We finally examine the scale effect of reservoirs and show that the increase of the number of involved reservoirs need more work to be costed and meanwhile can produce more coherence so that more ergotropy can be extracted. The obtained features contribute to the understanding of thermodynamics in common reservoirs and would be useful in quantum technologies when common reservoirs are necessary.