On First-Order Phase Transitions in Canonical and Grand Ensembles

Abstract

S. Katsura has found evidence from exact calculations on finite systems that has led him to suggest that, contrary to the generally accepted view, a van der Waals type loop will be found in an exact application of the canonical ensemble to a first-order phase transition. It is shown here that Katsura's results can be understood in terms of interfacial free energy in the two-phase region. A loop is indeed obtained, but it is not of the van der Waals type. In particular, the loop vanishes in the limit of an infinite system. The well-known argument of van Hove showing that a loop does not exist in an infinite system (canonical ensemble) is discussed in this connection.