This paper reviews a number of fundamental connections that exist between
nonequivalent microcanonical and canonical ensembles, the appearance of
first-order phase transitions in the canonical ensemble, and thermodynamic
metastable behavior.Comment: 4 pages, RevTeX, 1 figure. Contribution to the Proceedings of the
31st Workshop of the International School of Solid State Physics
``Complexity, Metastability and Nonextensivity'', held at the Ettore Majorana
Foundation and Centre for Scientific Culture, Erice, Sicily, Italy, July
2004. Edited by C. Tsallis, A. Rapisarda and C. Beck. To be published by
World Scientific, 200