Entropy Production — Irreversible Thermodynamics
Heat conduction, diffusion, Onsager reciprocal relations, σ ≥ 0
σ (entropy prod rate): — [W/K]
J_q (heat flux): —
J_D (diffusion flux): —
Temperature & concentration field
Entropy production rate σ(x,t)
Irreversible thermodynamics (Onsager, 1931): Near equilibrium, fluxes depend linearly on thermodynamic forces: J_q = L₁₁·X_T + L₁₂·X_μ (heat) and J_D = L₂₁·X_μ + L₂₂·X_T (mass). Onsager proved L₁₂=L₂₁ (reciprocal relations) from microscopic time-reversal symmetry. The entropy production rate σ = Σ Jᵢ·Xᵢ ≥ 0 always. Coupling (L₁₂≠0) gives Soret effect (temp gradient drives diffusion) and Dufour effect (conc gradient drives heat flow). The simulation evolves T(x) and c(x) on a 1D bar with Fourier+Fick+Soret/Dufour coupling.