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A relation giving a minimum for the irreversible work in quasi-equilibriumprocesses was derived by Sekimoto et al. (K. Sekimoto and S. Sasa, J. Phys.Soc. Jpn. {\bf 66} (1997), 3326) in the framework of stochastic energetics.This relation can also be written as a type of "uncertainty principle" in sucha way that the precise determination of the Helmholtz free energy through theobservation of the work $<W>$ requires an indefinitely large experimental time$\Delta t$. In the present article, we extend this relation to the case ofquasi-steady processes by using the concept of non-equilibrium Helmholtz freeenergy. We give a formulation of the second law for these processes thatextends that presented by Sekimoto (K. Sekimoto, Prog. Theo. Phys. Suppl. No.{\bf 130} (1998), 17) by a term of the first order in the inverse of theexperimental time. As application of our results, two possible experimentalsituations are considered: stretching of a RNA molecule and the drag of adipolar particle in the presence of a gradient of electric force.

Complementarity relation for irreversible processes near steady states