Schmidt H-J, Schnack J, Gemmer J. Stochastic thermodynamics of a finite quantum system coupled to a heat bath. Zeitschrift für Naturforschung A. 2021;76(8):731-745.
The consistent definition of the thermodynamic functions of small open quantum systems in contact with an environment in equilibrium with a heat bath has been the subject of many debates in the quantum community. In the present work we reproduce and comment parts of a recent approach of this subject by Rivas [15]. This approach overcomes the controversial discussions generated by the coupling between a system and its environment for any type of coupling between the two parts and allows for a consistent description of the thermodynamical properties of the system strongly interacting with the bath
Abstract We consider a situation where an N-level system (NLS) is coupled to a heat bath without being necessarily thermalized. For this situation, we derive general Jarzynski-type equations and conclude that heat and entropy is flowing from the hot bath to the cold NLS and, vice versa, from the hot NLS to the cold bath. The Clausius relation between increase of entropy and transfer of heat divided by a suitable temperature assumes the form of two inequalities which have already been considered in the literature. Our approach is illustrated by an analytical example.
-level system (NLS) is coupled successively to two heat baths with different temperatures without being necessarily thermalized and approaches a steady state. For this situation we apply a general Jarzynski-type equation and conclude that heat and entropy is flowing from the hot bath to the cold one. The Clausius relation between increase of entropy and transfer of heat divided by a suitable temperature assumes the form of two inequalities. Our approach is illustrated by an analytical example. For the linear regime, i.e., for small temperature differences between the two heat baths, we derive an expression for the heat conduction coefficient.