Van der Waals type loop in microcanonical caloric curves of finite systems.
The entropy is usually related to the energy density of states. This relation is approximate for the finite systems (clusters) and an exact relation connects the entropy with the phase volume of the system. These relations give the same results only in the thermodynamic limit. We consider the microcanonical caloric curves determined via both the approximate and exact relations. It is proved that if the caloric curve obtained from the exact relation has a van der Waals type loop (or S bend), then the caloric curve obtained from the approximate relation has S-bend, and the reverse statement is not correct. Using properties of the system at low and high energies we have shown that a van der Waals type loop in the caloric curve of the finite system requires a positive value of the second derivative of the logarithm of the canonical total energy distribution function at least at one value of the energy. The latter is the weaker necessary condition for S-bend to occur in the caloric curve than that obtained earlier.
Umirzakov
I H
IH
Institute of Thermophysics, Novosibirsk 630090, Russia.