Quantum thermodynamics of single particle systems

Classical thermodynamics is built with the concept of equilibrium states. However, it is less clear how equilibrium thermodynamics emerges through the dynamics that follows the principle of quantum mechanics. In this paper, we develop a theory to study the exact nonequilibrium thermodynamics of quantum systems that is applicable to arbitrary small systems, even for single particle systems, in contact with a reservoir. We generalize the concept of temperature into nonequilibrium regime that depends on the detailed dynamics of quantum states. When we apply the theory to the cavity system and the two-level atomic system interacting with a heat reservoir, the exact nonequilibrium theory unravels unambiguously (1) the emergence of classical thermodynamics from quantum dynamics in the weak system-reservoir coupling regime, without introducing equilibrium hypothesis; (2) the breakdown of classical thermodynamics in the strong coupling regime, which is induced by non-Markovian memory dynamics; and (3) the occurrence of dynamical quantum phase transition characterized by inflationary dynamics associated with a negative nonequilibrium temperature, from which the third law of thermodynamics, allocated in the deep quantum realm, is naturally proved. The corresponding dynamical criticality provides the border separating the classical and quantum thermodynamics. The inflationary dynamics may also provide a simple picture for the origin of big bang and universe inflation.