Complementarity relation for irreversible processes near steady states

Details Complementarity relation for irreversible processes near steady states Complementarity relation for irreversible processes near steady states

2012-01-03

arxiv.org/abs/1201.0923v2

Physics

Condensed Matter

Statistical Mechanics

14 pages, Corrected version

Scientific paper

A relation giving a minimum for the irreversible work in quasi-equilibrium processes was derived by K. 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 such a way that the precise determination of the Helmholtz free energy through the observation of the work $$ requires an indefinitely large experimental time $\Delta t$. 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 by a term of the first order in the inverse of the experimental time. We apply the results to a simple model.

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