COEXISTENCE IN FINITE SYSTEMS

We derive necessary conditions for finite systems to exhibit two local ly stable states with respect to fluctuations in the microcanonical an d canonical ensembles. The requirements are, respectively, that there be two inflections in the logarithm of the probability distribution of the energy or the number of particles in the canonical or grand canon ical ensembles. The thermodynamics associated with the whole phase spa ce may be related to quantities averaged over regions of phase space a nd are consistent with van Hove's theorem.