## Abstract

Thermodynamic speed limits are a set of classical uncertainty relations that, so far, place global bounds on the stochastic dissipation of energy as heat and the production of entropy. Here, instead of constraints on these thermodynamic costs, we derive integral speed limits that are upper and lower bounds on a thermodynamic benefit—the minimum time for an amount of mechanical work to be done on or by a system. In the short time limit, we show how this extrinsic timescale relates to an intrinsic timescale for work, recovering the intrinsic timescales in differential speed limits from these integral speed limits and turning the first law of stochastic thermodynamics into a first law of speeds. As physical examples, we consider the work done by a flashing Brownian ratchet and the work done on a particle in a potential well subject to external driving.

Original language | English |
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Article number | 05LT01 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 56 |

Issue number | 5 |

DOIs | |

State | Published - 3 Feb 2023 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2023 The Author(s). Published by IOP Publishing Ltd.

### Funding

This material is based upon work supported by the National Science Foundation under Grant No. 1856250. J R G acknowledges helpful conversations with Sky Nicholson and Luis Pedro García-Pintos.

Funders | Funder number |
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National Science Foundation | 1856250 |

## Keywords

- nonequilibrium statistical mechanics
- stochastic thermodynamics
- thermodynamic speed limits