The correlational entropy production during the local relaxation in a many body system with Ising interactions

TL;DR

This paper investigates the local relaxation and entropy production in finite many-body quantum systems with Ising interactions, revealing that total correlations grow monotonically and relate to thermodynamic entropy, with recurrence effects due to finite size.

Contribution

It introduces the concept of correlational entropy production during local relaxation in finite Ising systems, linking quantum correlations to thermodynamic irreversibility.

Findings

Total correlation exhibits a monotonic increasing envelope during relaxation.

Maximum total correlation aligns with exact time-dependent evolution results.

Recurrence appears after a typical time due to finite size effects.

Abstract

Isolated quantum systems follow the unitary evolution, which guarantees the full many body state always keeps a constant entropy as its initial one. In comparison, the local subsystems exhibit relaxation behavior and evolve towards certain steady states, which is called the local relaxation. Here we consider the local dynamics of finite many body system with Ising interaction. In both strong and weak coupling situations, the local observables exhibit similar relaxation behavior as the macroscopic thermodynamics; due to the finite size effect, recurrence appears after a certain typical time. Especially, we find that the total correlation of this system approximately exhibits a monotonic increasing envelope in both strong and weak coupling cases, which corresponds to the irreversible entropy production in the standard macroscopic thermodynamics. Moreover, the possible maximum of such total correlation calculated under proper constraints also coincides well with the exact result of time dependent evolution.