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, ${\overline{S}}_e/k_B\ge 1/2\mathrm{\Delta }t$, and its inverse is the minimum time to execute the process, $\mathrm{\Delta }t\ge k_B/2{\overline{S}}_e$. 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, $\overline{Q}\mathrm{\Delta }t\ge k_{B}T/2$. These bounds constrain the relationship between dissipation and time during nonstationary processes, including transient excursions from steady states.

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• Chaos
• Classical mechanics
• Classical statistical mechanics
• Dissipative dynamics
• Fluctuation theorems
• Irreversible processes
• Nonequilibrium & irreversible thermodynamics
• Nonequilibrium statistical mechanics