Maximum speed of dissipation

We derive statistical-mechanical speed limits on dissipation from the classical, chaotic dynamics of many-particle systems. In one, the rate of irreversible entropy production in the environment is the maximum speed of a deterministic system out of equilibrium, ${\bar{S}}_e\mathrm{/}{k}_B\ge 1\mathrm{/}2\mathrm{\Delta }t$, and its inverse is the minimum time to execute the process, $\mathrm{\Delta }t\ge k_B\mathrm{/}2{\bar{S}}_e$. Starting with deterministic fluctuation theorems, we show there is a corresponding class of speed limits for physical observables measuring dissipation rates. For example, in many-particle systems interacting with a deterministic thermostat, there is a trade-off between the time to evolve between states and the heat flux, $\bar{Q}\mathrm{\Delta }t\ge k_{B}T\mathrm{/}2$. These bounds constrain the relationship between dissipation and time during nonstationary process, including transient excursions from steady states.