Complementarity Relation for Irreversible Process Derived from Stochastic Energetics

Abstract

When the process of a system in contact with a heat bathis described by the classicalLangevin equation, use of the method of stochastic energetics [K. Sekimoto: J. Phys. Soc. Jpn. 66 (1997) 1234]enables us to derive the form of Helmholtz free energy and thedissipation function of the system.We are able toprove that the irreversible heat Q_irr and the time lapseΔ t of an isothermal process obey the complementarity relation, Q_irr , Δ t≥q k_BT , S_min, where S_min depends on the initial and the final values of the control parameters, but does not depend on the pathway between these values.