Strong Coupling Quantum Thermodynamics with Renormalized Hamiltonian and Temperature

We develop the strong coupling quantum thermodynamics based on the solution of the exact master equation. We find that both the Hamiltonian and the temperature must be renormalized due to the system-reservoir couplings. With the renormalized Hamiltonian and temperature, the exact steady state of open quantum systems can be expressed as a standard Gibbs state. The exact steady-state particle distributions obey the Bose-Einstein distribution or the Fermi-Dirac distribution only for the renormalized energy and temperature. In this formulation, heat and work are quantum mechanically defined, from which we compute the specific heat and examine the consistency of the theory. Consequently, thermodynamic laws and statistical mechanics emerge naturally and rigorously from quantum evolution of open systems.