Work and heat of a quantum system far from its equilibrium state

In this paper, we give a computational approach of work and heat for any quantum systems. We use the strategy that the part of energy exchange with the von Neumann entropy unchanging is defined as work, and the part with the von Neumann entropy changing is defined as heat. We define the work and heat and they are formulated. This method is suitable for the study of any quantum systems (not only bipartite quantum systems, but also single-body, and multi-body quantum systems). As examples, firstly we investigate a bipartite model whose dynamics can be rigorously solved by using the Bloch equation, and secondly, we study two single-body models by using the numerical method of master equation of Redfield form.