COMPLEMENTARITY RELATION FOR IRREVERSIBLE PROCESS DERIVED FROM STOCHASTIC ENERGETICS

When the process of a system in contact with a heat bath is described by the classical Langevin equation, use of the method of stochastic en ergetics [K. Sekimoto: J. Phys. Soc. Jpn. 66 (1997) 1234] enables us t o derive the form of Helmholtz free energy and the dissipation functio n of the system. We are able to prove that the irreversible heat Q(irr ) and the time lapse Delta t of an isothermal process obey the complem entarity relation, Q(irr) Delta t greater than or equal to k(B)T S-min , where S-min depends on the initial and the final values of the contr ol parameters, but does not depend on the pathway between these values .