Entropy Production & Fluctuation Theorem

Stochastic particle in a tilted periodic potential. The Gallavotti-Cohen fluctuation theorem: P(ΔS)/P(-ΔS) = exp(ΔS) — entropy-decreasing trajectories are exponentially rare but possible.

Parameters

Force F 0.50 Temperature T 1.00 Potential V₀ 1.50 Particles N 40 τ window 20

Particles: 40
Mean ΔS: 0.00
Neg entropy: 0.0%
FT slope: 1.00 (theory: 1.0)

Fluctuation Theorem:
P(ΔS)/P(-ΔS) = e^ΔS

ln[P(+σ)/P(-σ)] = σ

Jarzynski equality:
⟨e^(-W/T)⟩ = e^(-ΔF/T)

2nd law: ⟨ΔS⟩ ≥ 0, but
individual ΔS < 0 allowed!