Dissipation production in a closed two-level quantum system as a test of the obversibility of the dynamics

TL;DR

This paper investigates irreversibility in a closed two-level quantum system by evaluating dissipation production, testing obversibility, and analyzing conditions for time-asymmetric behavior through numerical simulations.

Contribution

It introduces a method to compute dissipation production in a closed quantum system and explores its relation to obversibility and fluctuation theorems, providing new insights into quantum irreversibility.

Findings

Dissipation production can be evaluated in a simple quantum system.

Conditions for time-asymmetric behavior are identified.

Some cases satisfy the Evans-Searles Fluctuation Theorem.

Abstract

Irreversible behaviour is traditionally associated with open stochastic dynamical systems, but an asymmetry in the probabilistic specification of a closed deterministic system can similarly lead to a disparity between the likelihoods of a particular forward and corresponding backward behaviour starting from a specified time. Such a comparison is a test of a property denoted obversibility, which may be quantified in terms of dissipation production as a measure of irreversibility. We here discuss the procedure needed to evaluate dissipation production in a simple, deterministic two-level quantum system described by a statistical ensemble of state vectors and then provide numerical results for illustrative situations. We consider cases that both do and do not fulfill an Evans-Searles Fluctuation Theorem for the dissipation production, and identify conditions for which the system will display time-asymmetric average behaviour as it evolves.