Ergotropy-based quantum thermodynamics

We introduce an ergotropy-based formulation of quantum thermodynamics, which provides a strong connection between average heat and von Neumann entropy. By adopting this formulation, we can reinterpret the infinitesimal average heat in terms of the infinitesimal change of the passive state associated with the density operator behind the quantum dynamics. Like entropy, this leads to a heat concept that is invariant under passive state transformations. As an application, the average heat can be used as a general non-Markovianity measure for unital maps. Moreover, a positive-semidefinite temperature naturally emerges in an out-of-equilibrium ergotropy-based scenario. Concerning the infinitesimal average work, it arises as an infinitesimal variation of ergotropy, as well as an extra passive work contribution in the case of a time-dependent Hamiltonian. As illustrations, we consider the thermodynamics of a single-qubit open system in the cases of generalized amplitude-damping and phase-damping channels.