  I discuss the validity of a result put forward recently by Chomaz and
Gulminelli [Physica A 330 (2003) 451] concerning the equivalence of two
definitions of first-order phase transitions. I show that distributions of
zeros of the partition function fulfilling the conditions of the Yang-Lee
Theorem are not necessarily associated with nonconcave microcanonical entropy
functions or, equivalently, with canonical distributions of the mean energy
having a bimodal shape, as claimed by Chomaz and Gulminelli. In fact, such
distributions of zeros can also be associated with concave entropy functions
and unimodal canonical distributions having affine parts. A simple example is
worked out in detail to illustrate this subtlety.

Statistical Mechanics