Thermodynamic Cost of Random-Time Protocols

TL;DR

This paper resolves apparent thermodynamic violations in systems driven by random-time protocols by demonstrating that memory erasure costs uphold the second law, linking temporal information with thermodynamics.

Contribution

It introduces a framework connecting random timing protocols, memory costs, and thermodynamics, clarifying how the second law is preserved.

Findings

Memory erasure work exceeds protocol work on average

Random timing protocols do not violate thermodynamics when accounting for memory costs

Concrete setups measure random times without continuous monitoring

Abstract

Systems that are driven by a randomly timed, external protocol can seemingly violate the second law of thermodynamics. We show that this thermodynamic paradox is resolved if the outcome of the random time is stored in a memory device. Specifically, we show that the average work required to erase the memory is always larger than the average work gained from the protocol. We also discuss concrete setups that measure random times directly without continuous monitoring. Taken together, this paper discusses the relationship between temporal information and thermodynamics. This framework is relevant for external protocols employing random times, such as, stochastic resetting protocols and cyclically driven heat engines that use randomly timed protocols.