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Fluctuations of charged particle number are studied in the canonical ensemble. In the infinite volume limit the fluctuations in the canonical ensemble are different from the fluctuations in the grand canonical one. Thus, the well-known equivalence of both ensembles for the average quantities does not extend for the fluctuations. In view of the possible relevance of the results for the analysis of fluctuations in nuclear collisions at high energies, a role of the limited kinematical acceptance is studied.

Thermodynamical properties of nuclear matter undergoing multifragmentation are studied within a simplified version of the statistical model. An exact analytical solution has been found for the grand canonical ensemble. Excluded volume effects are taken into account in the thermodynamically self-consistent way. In thermodynamic limit the model exhibits a first order liquid-gas phase transition with specific mixed phase properties. An extension of the model including the Fisher's term is also studied. The possibility of the second order phase transition at or above the critical point is demonstrated. The fragment mass distributions in the different regions of the phase diagram are discussed.