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, $\bar S_e/k_B\geq 1/2\Delta t$, and its inverse is the minimum time to execute the process, $\Delta t\geq k_B/2\bar S_e$. 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, $\bar{Q}\Delta t\geq k_BT/2$. These bounds constrain the relationship between dissipation and time during nonstationary process, including transient excursions from steady states.