Thermodynamic speed limits for mechanical work

TL;DR

This paper introduces integral thermodynamic speed limits that bound the minimum time required for mechanical work, providing a new perspective on the relationship between thermodynamics and timescales in stochastic systems.

Contribution

It derives integral speed limits for mechanical work, connecting intrinsic and extrinsic timescales, and extends the first law of thermodynamics into a first law of speeds.

Findings

Derived bounds on work timescales in stochastic systems

Connected intrinsic and extrinsic thermodynamic timescales

Applied results to Brownian ratchets and driven particles

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.