Stochastic Thermodynamics: Driven Ratchet

A Brownian particle in a tilted periodic potential. Track work W, heat Q, free energy ΔF, and entropy production Σ = βW − βΔF ≥ 0. Verify the Crooks fluctuation theorem.

Applied force F0.50
Temperature k_BT0.30
Potential barrier V₀1.00
Simulation steps5000
Number of trajectories200
Running...
Overdamped Langevin: dx = [−V'(x) + F] dt + √(2k_BT) dW
Potential: V(x) = V₀ sin(2πx) − F·x (sawtooth ratchet)
Entropy production: Σ = β(W − ΔF) = β∫F dx ≥ 0 (2nd law)
Jarzynski equality: ⟨e^(−βW)⟩ = e^(−βΔF) (even far from equilibrium)
Crooks FT: P(Σ)/P(−Σ) = e^Σ — histogram shows this ratio in log scale.