Lower bounds for the mean dissipated heat in an open quantum system

TL;DR

This paper investigates lower bounds on the mean dissipated heat in open quantum systems, comparing entropic and thermodynamic bounds and analyzing their dependence on initial states, with implications for quantum thermodynamics.

Contribution

It extends the comparison of heat dissipation bounds to open quantum systems with infinite recurrence times, revealing their dependence on initial state properties.

Findings

Thermodynamic bound is independent of initial coherence.

Entropic bound depends on initial coherence and population.

Purity of initial state determines which bound is tighter.

Abstract

Landauer's principle provides a perspective on the physical meaning of information as well as on the minimum working cost of information processing. Whereas most studies have related the decrease in entropy during a computationally irreversible process to a lower bound of dissipated heat, recent efforts have also provided another lower bound associated with the thermodynamic fluctuation of heat. The coexistence of the two conceptually independent bounds has stimulated comparative studies of their close relationship or tightness; however, these studies were concerned with finite quantum systems that allowed the revival of erased information because of a finite recurrence time. We broaden these comparative studies further to open quantum systems with infinite recurrence times. By examining their dependence on the initial state, we find the independence of the thermodynamic bound from the initial coherence, whereas the entropic bound depends on both the initial coherence and population. A crucial role is indicated by the purity of the initial state: the entropic bound is tighter when the initial condition is sufficiently mixed, whereas the thermodynamic bound is tighter when the initial state is close to a pure state. These trends are consistent with previous results obtained for finite systems.