Complementarity relation for irreversible processes near steady states

A relation giving a minimum for the irreversible work in quasi-equilibrium processes was derived by Sekimoto et al. [K. Sekimoto, S. Sasa, J. Phys. Soc. Japan 66 (1997) 3326] in the framework of stochastic energetics. This relation can also be written as a type of “uncertainty principle” in such a way that the precise determination of the Helmholtz free energy through the observation of the work 〈 W 〉 requires an indefinitely large experimental time Δ t . In the present article, we extend this relation to the case of quasi-steady processes by using the concept of non-equilibrium Helmholtz free energy. We give a formulation of the second law for these processes that extends that presented by Sekimoto [K. Sekimoto, Prog. Theoret. Phys. Suppl. No. 130 (1998) 17] by a term of the first order in the inverse of the experimental time. As an application of our results, two possible experimental situations are considered: stretching of a RNA molecule and the drag of a dipolar particle in the presence of a gradient of electric force.