Comparison between thermodynamic work and heat in autonomous quantum systems

One of the most important problems in quantum thermodynamics is how to distinguish work and heat in autonomous quantum systems. In this paper, work and heat are defined through the following criterion, i.e., work is the energy that cannot change the entropy of the energy resource, and satisfies the Jarzynski equality, while heat does not. Two kinds of definitions satisfying the two corresponding requirements are proposed and demonstrated, and the consistency condition of the two kinds is given. Through the first definition, the problem of entropy production is investigated. A model study is also presented to verify the proposal.