Emergence of a fluctuation relation for heat in nonequilibrium Landauer processes

TL;DR

This paper derives a fluctuation relation for heat in nonequilibrium quantum Landauer processes, showing that heat fluctuations are exponentially suppressed with system size and temperature, providing new bounds on dissipated heat.

Contribution

It introduces an emergent fluctuation relation for heat in nonequilibrium quantum processes, extending concentration of measure techniques to mixed states.

Findings

Heat fluctuations are exponentially suppressed with system size.

Average heat dissipation is guaranteed under certain conditions.

Results apply to large or high-temperature regimes.

Abstract

In a generalized framework for the Landauer erasure protocol, we study bounds on the heat dissipated in typical nonequilibrium quantum processes. In contrast to thermodynamic processes, quantum fluctuations are not suppressed in the nonequilibrium regime and cannot be ignored, making such processes difficult to understand and treat. Here we derive an emergent fluctuation relation that virtually guarantees the average heat produced to be dissipated into the reservoir either when the system or reservoir is large (or both) or when the temperature is high. The implication of our result is that for nonequilibrium processes, heat fluctuations away from its average value are suppressed independently of the underlying dynamics exponentially quickly in the dimension of the larger subsystem and linearly in the inverse temperature. We achieve these results by generalizing a concentration of measure relation for subsystem states to the case where the global state is mixed.