Time Evolution and Thermodynamics for the Nonequilibrium System in Phase-Space

Chen-Huan Wu

Published 2017-11-01Version 1

The integrable system is constrained strictly by the conservation law during the time evolution, and the nearly integrable system or nonintegrable system is also constrained by the conserved parameters (like the constants of motion) with corresponding generalized Gibbs ensemble (GGE) which is indubitability a powerful tool in the prediction of thr relaxation dynamics. For stochastic evolution dynamic with considerable noise, the obviously quantum or thermal correlations which don't exhibit the thermal behavior, (like the density of kinks or transverse magnetization correlators), display a asymptotic nonthermal behavior, in fact, it's a asymptotic quasisteady state with a infinte temperature and therefore the required distance to the nonthermal steady state is in a infinite time average. We unambiguously investigate the relaxation of a nonequilibrium system in a canonical ensemble and the temporal behavior of the many-body quantum system and macroscopic system, as well as the corresponding linear coupling between harmonic oscillators, Matric-method is utilized in entropy ensemble to discuss the boundary and diagonalization, the approximation by perturbation theory is also obtained.