An Introduction to the Thermodynamic and Macrostate Levels of   Nonequivalent Ensembles
  This short paper presents a nontechnical introduction to the problem of nonequivalent microcanonical and canonical ensembles. Both the thermodynamic and the macrostate levels of definition of nonequivalent ensembles are introduced. The many relationships that exist between these two levels are also explained in simple physical terms. 
H. Touchette, R.S. Ellis, B. Turkington