Dissipation in steady states of chemical systems and deviations from minimum entropy production

According to the linear thermodynamic theory of irreversible processes, entropy production is minimized at the steady states of nonequilibrium systems. The principle of minimum entropy production is obtained if the dissipation is expanded in the deviation δ from equilibrium, truncated to lowest order (δ2), and then differentiated. At this level of apprximation, the derivative of the dissipation is linear in δ and vanishes at the steady state. For a simple chemical reaction mechanism in a well-defined model system, we have derived the corrections to this approximation, by first evaluating the dissipation and its derivative exactly, and then expanding as a series in δ. To leading order in δ, the ratio of the derivative to the dissipation at the steady state is 12 (in dimensionless units), and this ratio does not decrease as equilibrium is approached. The steady state coincides with the state of minimum entropy production only at equilibrium. Given sufficient accuracy in measurements of species concentrations, the breakdown of the principle of minimum entropy production can be detected experimentally when the relative standard deviation in measurements of the dissipation is less than δ. Our example shows that the dissipation in a reaching chemical system may increase in time, in the later stages of relaxation toward a near-equilibrium steady state.