Complementary relation for irreversible processes near steady states

S.SANTINI; E.IZQUIERDO; M. F. CARUSELA

PHYSICA A - STATISTICAL AND THEORETICAL PHYSICS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2013 vol. 392 p. 4856 - 4867

0378-4371

A relation giving a minimum for the  irreversible work in quasi-equilibrium processes was derived by Sekimoto et al. (K. Sekimoto and S. Sasa, J. Phys. Soc. Jpn. {f 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 (K. Sekimoto, Prog. Theo. Phys. Suppl. No. {f 130} (1998), 17) by  a term of the first order in the inverse of the experimental time. We apply the results to a simple model.