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Classical thermodynamics is built with the concept of equilibrium states.However, it is less clear how equilibrium thermodynamics emerges through thedynamics that follows the principle of quantum mechanics. In this paper, wedevelop a theory to study the exact nonequilibrium thermodynamics of quantumsystems that is applicable to arbitrary small systems, even for single particlesystems, in contact with a reservoir. We generalize the concept of temperatureinto nonequilibrium regime that depends on the detailed dynamics of quantumstates. When we apply the theory to the cavity system and the two-level atomicsystem interacting with a heat reservoir, the exact nonequilibrium theoryunravels unambiguously (1) the emergence of classical thermodynamics fromquantum dynamics in the weak system-reservoir coupling regime, withoutintroducing equilibrium hypothesis; (2) the breakdown of classicalthermodynamics in the strong coupling regime, which is induced by non-Markovianmemory dynamics; and (3) the occurrence of dynamical quantum phase transitioncharacterized by inflationary dynamics associated with a negativenonequilibrium temperature, from which the third law of thermodynamics,allocated in the deep quantum realm, is naturally proved. The correspondingdynamical criticality provides the border separating the classical and quantumthermodynamics. The inflationary dynamics may also provide a simple picture forthe origin of big bang and universe inflation.

Quantum thermodynamics of single particle systems