Inverse linear versus exponential scaling of work penalty in finite-time bit reset

TL;DR

This paper investigates how the work penalty in finite-time bit reset protocols scales with time, revealing conditions under which it decreases exponentially versus inversely linearly, with analytical and numerical insights.

Contribution

It provides analytical results and simulations clarifying the conditions affecting exponential versus linear scaling of work penalties in finite-time bit reset.

Findings

Work penalty can scale exponentially or inversely linearly with protocol time.

Protocol parameters like error rate and energy shift influence the scaling behavior.

Analytical bounds and numerical examples illustrate the transition between scaling regimes.

Abstract

Bit reset is a basic operation in irreversible computing. This costs work and dissipates energy in the computer, creating a limit on speeds and energy efficiency of future irreversible computers. It was recently shown in [Phys. Rev. Lett. 127, 190602 (2021)] that for a finite-time reset protocol, the additional work on top of the quasistatic protocol can always be minimized by considering a two-level system, and then be lower bounded through a thermodynamical speed limit. An important question is to understand under what protocol parameters, including bit reset error and maximum energy shift, this penalty decreases exponentially vs inverse linearly in the protocol time. Here we provide several analytical results to address this question, as well as numerical simulations of specific examples of protocols.