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

TL;DR

This paper investigates the relaxation dynamics and thermodynamics of nonequilibrium many-body quantum systems, focusing on integrable and nonintegrable cases, and explores their asymptotic states and entropy properties using matrix methods.

Contribution

It provides a detailed analysis of relaxation processes in nonequilibrium systems, including the role of conserved quantities and the behavior of asymptotic nonthermal states.

Findings

Integrable systems are constrained by conservation laws during evolution.

Nonintegrable systems exhibit asymptotic nonthermalization with infinite temperature states.

Matrix methods in entropy ensembles help analyze boundary effects and diagonalization.

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.