Ergodic dissipation
Statement
In ergodic systems, the time average of a physical quantity equals its ensemble average. This allows statistical mechanics to equate entropy production with dissipation: the irreversible flow of energy to heat. Ergodicity bridges deterministic dynamics and probabilistic thermodynamics—when a system explores phase space uniformly, dissipation is the macroscopic manifestation of microscopic irreversibility.
Formula
⟨A⟩_time = ⟨A⟩_ensemble ⇒ dissipation ↔ entropy production
Equation
lim_{T→∞} (1/T) ∫₀ᵀ A(t) dt = ∫ A dμ (ergodic)
Source
Boltzmann (ergodic hypothesis 1870s), Kolmogorov–Sinai (ergodic theory 1950s–60s), Prigogine (dissipative structures)
Domains
physics, mathematics