Relaxing towards generalized one-body Boltzmann states

TL;DR

This paper investigates the local relaxation dynamics of an isolated quantum chain of three-level systems, showing that total correlation entropy approaches a maximum indicative of generalized one-body Boltzmann states, serving as a marker for irreversibility.

Contribution

It introduces the concept of generalized one-body Boltzmann states in a quantum chain and links total correlation entropy to the irreversibility of relaxation processes.

Findings

Total correlation entropy increases monotonically during relaxation.

Maximum correlation entropy corresponds to generalized one-body Boltzmann states.

Total correlation entropy effectively indicates dynamical irreversibility.

Abstract

Isolated quantum systems follow the reversible unitary evolution; if we focus on the dynamics of local states and observables, they exhibit the irreversible relaxation behaviors. Here we study the local relaxation process in an isolated chain consisting of \emph{N} three level systems. Though the entropy of the full many body state keeps a constant, it turns out the total correlation of this system approximately exhibits a monotonically increasing behavior. More importantly, a variation analysis shows that, the total correlation entropy would achieve its theoretical maximum when each site stays in a generalized one-body Boltzmann state, which is not solely determined by the energy but also depends on the spin value of each onsite level. It turns out such a theoretical correlation maximum is highly coincident with the result obtained from the exact time dependent evolution. In this sense, the total correlation entropy well serves as an indicator for the dynamical irreversibility of the nonequilibrium relaxation in this isolated system.