Abstract
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 of quantum thermodynamics that is applicable for arbitrary small systems, even for single particle systems coupled with a reservoir. We generalize the concept of temperature beyond equilibrium that depends on the detailed dynamics of quantum states. We apply the theory to a cavity system and a two-level system interacting with a reservoir, respectively. The results unravels (1) the emergence of thermodynamics naturally from the exact quantum dynamics in the weak system-reservoir coupling regime without introducing the hypothesis of equilibrium between the system and the reservoir from the beginning; (2) the emergence of thermodynamics in the intermediate system-reservoir coupling regime where the Born-Markovian approximation is broken down; (3) the breakdown of thermodynamics due to the long-time non-Markovian memory effect arisen from the occurrence of localized bound states; (4) the existence of dynamical quantum phase transition characterized by inflationary dynamics associated with negative dynamical temperature. The corresponding dynamical criticality provides a border separating classical and quantum worlds. The inflationary dynamics may also relate to the origin of big bang and universe inflation. And the third law of thermodynamics, allocated in the deep quantum realm, is naturally proved.
Highlights
Thermodynamics is built with the concept of equilibrium states
The dynamics of open quantum systems can be fully determined by the reduced quantum density matrix ρS(t), which is defined by tracing over all the reservoir degrees of freedom from the total density matrix ρtot(t) of the system plus the reservoirs: ρS(t) = Tr R[ρtot(t)]
To demonstrate the universality of the above finding in the simple cavity system described by the Fano-Anderson model, we investigate the quantum thermodynamics of another widely studied open quantum system, namely a two-level atomic system interacting with a bosonic reservoir, to see how thermodynamics emerges from quantum dynamics of spontaneous decay process
Summary
Thermodynamics is built with the concept of equilibrium states. it is less clear how equilibrium thermodynamics emerges through the dynamics that follows the principle of quantum mechanics. This solution in the weak system-reservoir coupling regime provides the foundation of the equilibrium thermodynamics, namely how thermalization is dynamically realized within the framework of a fully dynamical evolution of quantum mechanics.
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