Brownian Motor — Asymmetric Ratchet & Particle Transport

Büttiker-Landauer ratchet: a particle in an asymmetric sawtooth potential driven by thermal fluctuations from two reservoirs at temperatures T₁ and T₂. When T₁≠T₂, directed current emerges — the second law is not violated because entropy is produced.

Parameters

Langevin: γẋ = -dV/dx + √(2γkTᵢ)·ξ(t) V(x): sawtooth V₊=U₀/α (short side) V₋=U₀/(1-α) (long side) Current J ∝ (T₁-T₂) for α≠0.5 Reversal when T₁/T₂ crosses threshold