σ = J·X — flux times thermodynamic force drives entropy production
In linear nonequilibrium thermodynamics (Onsager, 1931), fluxes J_i = Σ L_ij X_j are linear in forces X. The entropy production rate σ = Σ J_i·X_i ≥ 0 (second law). Onsager's reciprocal relations: L_ij = L_ji (proven from microscopic time-reversal symmetry). The minimum entropy production principle (Prigogine) states that steady states minimize σ subject to constraints. Beyond the linear regime, dissipative structures (Bénard cells, chemical oscillations) can emerge.