Entropy-based formulation of thermodynamics in arbitrary quantum evolution

Given the evolution of an arbitrary open quantum system, we formulate a general and unambiguous method to separate internal energy change system into entropy-related contribution part causing no entropy change, identified as heat work, respectively. We also demonstrate that work admit geometric dynamical descriptions by developing universal equation for given trajectory system. The dissipative coherent parts this contribute exclusively where specific role from counterdiabatic drive is underlined. Next define expression irreversible production which does not have explicit dependence on properties ambient environment; rather, it depends set system's observables excluding its Hamiltonian independent change. illustrate our results with three examples.