The Fictitious Equilibrium Ensemble in the Theory of Quenched Disordered Systems

Abstract

A method proposed by Morita for calculating the thermodynamic properties of a quenched disordered system by equating it to a suitably chosen fictitious equilibrium ensemble in an enlarged phase space, is re-examined. It is shown that Morita’s prescription, in its original form, is incomplete in that it leaves the free energy of the fictitious ensemble entirely undefined. A missing postulate, named the “zero mean potential condition”, is found which must supplement the Morita condition for a full specification of the fictitious ensemble to be achieved. The formulation thus obtained is shown to be thermodynamically self-consistent up to first order in the derivatives of the free energy, and to be equivalent to the maximum entropy formalism proposed by Mazo. The resulting free energy is, except for an irrelevant entropic contribution, equal to the Brout-Vuillermot “quenched” free energy.