Energy conservation, counting statistics, and return to equilibrium

摘要: We study a microscopic Hamiltonian model describing an N-level quantum sys- tem S coupled to infinitely extended thermal reservoir R. Initially, the system is in arbitrary state while equilibrium at inverse temperature β. Assuming that +R mixing with respect joint equi- librium state, we Full Counting Statistics (FCS) of energy transfers →R and R →S process return equilibrium. The first FCS describes increase S. It atomic probability measure, denoted PS,λ,t, con- centrated on set differences sp(HS ) −sp(HS (HS S, t length time interval during which measurement transfer performed, λ strength interaction between R). second FCS, PR,λ,t, decrease typically continu- ous measure whose support whole real line. large limit →∞ these two measures followed by weak coupling →0 prove limiting coincide. This result strengthens law thermodynamics for open systems. proofs are based modular theory operator algebras representation PR,λ,t operators.