PHASE TRANSITIONS WITHOUT THERMODYNAMIC LIMIT The Crucial Rôle of Possible and Impossible Fluctuations The Treatment of Inhomogeneous Scenaria in the Microcanonical Ensemble

“In the thermodynamic limit the canonical and the microcanonical ensemble are equivalent in all details and generality. ” Statements like this are found in many textbooks of statistical thermodynamics. It is the purpose of this contribution to show that this is not so, and, more importantly, that the microcanonical ensemble allows for significant insight into the mechanism of first order phase-transitions which is hidden in the canonical ensemble. E.g.: at the liquid-gas transition under given pressure large and fluctuating spatial inhomogeneities are created. This surface entropy Ssurf governs the surface tension. At the critical point TcrSsurf compensates even the surface energy of the ground state leading to the vanishing of the surface tension. In the canonical ensemble at given pressure, however, inhomogeneities become suppressed by ∼ e−N2/3fsurf/Tboil , (1)