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

Abstract

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 nonthermalization, and in fact it's a asymptotic quasisteady state with a infinte temperature, therefore the required distance to the nonthermal steady state is in a infinite time average. In this paper, we unambiguously investigate the relaxation of a nonequilibrium system in a canonical ensemble for integrable system or nonintegrable system, and the temporal behavior of many-body quantum system and the macroscopic system, as well as the corresponding linear-coupling between harmonic oscillators. Matrix-method in entropy ensemble is also utilized to discuss the boundary and the important diagonalization, the approximation by the perturbation theory is also obtained.

51 pages, 14 figures

References in corpus (6)

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• Dynamical Axion Field in Topological Magnetic Insulators
• Optimal measurements for simultaneous quantum estimation of multiple phases
• Thermodynamic Bounds on Precision in Ballistic Multi-Terminal Transport
• Spatial entanglement of bosons in optical lattices
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Cited by in corpus (6)

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• Tight-binding model and ab initio calculation of silicene with strong spin-orbit coupling in low-energy limit
• Many-electron effect to the dynamical polarization of silicene-like two-dimension Dirac materials
• Josephson effect in silicene-based SNS Josephson junction: Andreev reflection and free energy
• Electronic transport and dynamical polarization in bilayer silicene-like system
• Dynamical polarization and the optical response of silicene and related materials