Nonperturbative renormalization of quantum thermodynamics from weak to strong couplings

Wei-Ming Huang^1*, Wei-Min Zhang¹

¹Department of Physics, National Cheng Kung University, Tainan, Taiwan

* Presenter:Wei-Ming Huang, email:huangoazo@gmail.com

Quantum thermodynamics of strong coupling faces two difficulties: (i) How to determine the internal energy of a strong coupling system (ii) How to correctly calculate entropy production? We define the internal energy by the renormalization Hamiltonian, as it contains all the renormalization effects due to the environment. We also introduced the renormalization temperature to calculate the entropy production. In the steady-state limit, regardless of the strength of the coupling, the exact solution of the reduced density matrix is the Gibbs-type state and can be expressed as the standard Gibbs state with renormalized quantities. At the weak coupling limit, the renormalized Hamiltonian and the renormalized temperature are reduced to the original Hamiltonian of the system and the initial temperature of the reservoir. Thus, classical thermodynamics and statistical mechanics appear naturally in the dynamics of open quantum systems. Beyond more, all laws in statistical mechanics are preserved even in strong coupling.

Keywords: Strong coupling quantum thermodynamics, Non-equilibrium statistical mechanics, Open quantum system, Quantum master equation , Green's function methods