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Thermodynamic cost of random-time protocols

Izaak Neri

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Phys. Rev. E 112, 044114 – Published 9 October, 2025

DOI: https://doi.org/10.1103/8dmt-256h

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.

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Phys. Rev. E 112, 044114– Published 9 October, 2025
  • Received 2 January 2025
  • Revised 1 July 2025
  • Accepted 19 September 2025
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