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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.
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This content will become publicly available on March 1, 2026
Dissipation rates from experimental uncertainty
Active matter and driven systems exhibit statistical fluctuations in density and particle positions that are an indirect indicator of dissipation across length and time scales. Here, we quantitatively relate these fluctuations to a thermodynamic speed limit that constrains the rates of heat and entropy production in nonequilibrium processes. By reparametrizing the speed limit set by the Fisher information, we show how to infer these dissipation rates from directly observable or controllable quantities. This approach can use available experimental data as input and avoid the need for analytically solvable microscopic models or full time-dependent probability distributions. The heat rate we predict agrees with experimental measurements for a pulled Brownian particle and a microtubule active gel, which validates the approach and suggests potential for the design of experiments.
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- Award ID(s):
- 2231469
- PAR ID:
- 10620717
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review Research
- Volume:
- 7
- Issue:
- 1
- ISSN:
- 2643-1564
- Page Range / eLocation ID:
- L012078
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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