Entropy Production — Non-Equilibrium Driven System

A colloidal particle driven by a non-equilibrium force dissipates entropy at rate σ = J·F/T. Visualize how dissipation and probability currents emerge far from equilibrium.

Entropy production rate σ
σ = 0.000
Mean velocity ⟨v⟩
⟨v⟩ = 0.000
Jarzynski: ⟨e^{-W/T}⟩=e^{-ΔF/T}
Stochastic thermodynamics (Sekimoto 1997, Seifert 2005): each trajectory carries a well-defined entropy production. For a particle in a tilted potential V(x)+Fx:

σ = J · F / T where J = ⟨v⟩ = F/γ is the steady-state current.

The second law demands σ ≥ 0; equality only at equilibrium (F=0). Entropy production maps the "arrow of time" in the microscopic dynamics.