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

Irreversible behavior in open stochastic dynamical systems is quantified by stochastic entropy production, a property that measures the difference in likelihoods of forward and subsequent backward system evolution. But for a closed system, governed by deterministic dynamics, such an approach is not appropriate. Instead, we can consider the difference in likelihoods of forward and obverse behavior: the latter being a backward trajectory initiated at the same time as the forward trajectory. Such a comparison allows us to define dissipation production, an analog of stochastic entropy production. It quantifies the breakage of a property of the evolution termed obversibility just as stochastic entropy production quantifies a breakage of reversibility. Both are manifestations of irreversibility. In this study we discuss dissipation production in a quantum system. We consider a simple, deterministic, two-level quantum system characterized by a statistical ensemble of state vectors, and we provide numerical results to illustrate the ideas. We consider cases that both do and do not satisfy an Evans-Searles Fluctuation Theorem for the dissipation production, and hence identify conditions under which the system displays time-asymmetric average behavior: an arrow of time.

Automated summary

In this study, dissipation production in a quantum system is discussed. A simple, deterministic, two-level quantum system characterized by a statistical ensemble of state vectors is considered, and numerical results are provided to illustrate the ideas. Cases that both do and do not satisfy an Evans-Searles Fluctuation Theorem for the dissipation production are considered, identifying conditions under which the system displays time-asymmetric average behavior: an arrow of time.