  Microcanonical thermodynamics (MCTh) is contrasted to canonical
thermodynamics (CTh). At phase transitions of 1.order the two ensembles are NOT
equivalent even in the thermodynamic limit . Energy fluctuations do not vanish
and phase separations are suppressed in CTh. A proper treatment of fluctuations
is neccessary. MCTh allows to address even isolated small systems where phase
transitions can be clearly classified into first order and continuous ones. The
microcanonical caloric curve T(E) determines the transition temperature, latent
heat AND surface entropy/tension. For systems of ca.1000 Na-, K-, or Fe-atoms
at 1 atm. all 3 quantities can be calculated. The three parameters approach
with rising size the known bulk values. There is nothing that demands the use
of the thermodynamic limit. Within microcanonical thermodynamics of finite
systems there are fundamental differences between conserved extensive variables
and ensemble related ones like entropy, temperature and pressure. This is
discussed in detail.

Statistical Mechanics;Nuclear Theory