Microcanonical vs. canonical thermodynamics
The microcanonical ensemble is in important physical situations different from the canonical one even in the thermodynamic limit. In contrast to the canonical ensemble it does not suppress spatially inhomogeneous configurations like phase separations. It is shown how phase transitions of first order can be defined and classified unambiguously for finite systems without the use of the thermodynamic limit. It is further shown that in the case of the 10-states Potts model as well for the liquid-gas transition in Na, K, and Fe the microcanonical transition temperature, latent heat and interphase surface tension are similar to their bulk values for $\sim 200-3000$ particles. For Na and K the number of surface atoms keeps approximately constant over most of the transition energies because the evaporation of monomers is compensated by an increasing number of fragments with $\ge 2$ atoms (multifragmentation).