Nonequilibrium Steady-State Entropy Production

Driven diffusion: particles flowing under force and temperature gradient

Drive

Entropy Production Rate

σ̇ (total) = 0.00 kB/s
σ̇ (force) = 0.00 kB/s
σ̇ (heat) = 0.00 kB/s
⟨J⟩ flux = 0.00
2nd law: σ̇ ≥ 0 → ✓
Physics: In a nonequilibrium steady state (NESS), a system is maintained out of equilibrium by external drives (forces, temperature gradients). Unlike equilibrium, detailed balance is broken and entropy is continuously produced at rate σ̇ = J·F/T > 0 (Schnakenberg 1976). Here particles diffuse under a tilted periodic potential with a temperature gradient — the left half is hot (Th), right half cold (Tc). The entropy production rate splits into contributions from the mechanical force (σ̇F = J·F) and heat flows (σ̇Q = Q̇·(1/Tc−1/Th)). The second law guarantees σ̇ ≥ 0 always.