Non-Equilibrium Steady State & Probability Current

Overdamped Langevin · Washboard potential · Stall force · Carnot efficiency

Tilted washboard potential V(x) = V₀sin(2πx) − Fx

Steady-state probability density ρ(x) and current J

Particle ensemble (200 overdamped Brownian particles)

Parameters

Mean current J:
Direction:
Power input P=FJ:
Entropy prod. σ:
Efficiency η:
Fokker-Planck: ∂ₜρ = −∂ₓJ
J = −D∂ₓρ − (D/T)ρ∂ₓV
NESS: J = const ≠ 0, ρ ≠ e^(-V/T)/Z
Stall: F* = V₀·2π (Kramers rate balance)