Maximum speed of dissipation

Swetamber Das, Jason R. Green

Published 2023-05-20Version 1

Physical systems powering motion or creating structure in a fixed amount of time dissipate energy and produce entropy. Here, we derive speed limits on dissipation from the classical, chaotic dynamics of many-particle systems: the inverse of the entropy irreversibly produced bounds the time to execute a physical process for deterministic systems out of equilibrium, $\Delta t\geq k_B/\bar s_i$. We relate this statistical-mechanical speed limit on the mean entropy rate to deterministic fluctuation theorems. For paradigmatic classical systems, such as those exchanging energy with a deterministic thermostat, there is a trade-off between the time to evolve to a distinguishable state and the heat flux, $\bar{q}\Delta t\geq k_BT$. In all these forms, the inequality constrains the relationship between dissipation and time during any nonstationary process including transient excursions from steady states.