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We calculate exactly both the microcanonical and canonical thermodynamicfunctions (TDFs) for a one-dimensional model system with piecewise constantLennard-Jones type pair interactions. In the case of an isolated $N$-particlesystem, the microcanonical TDFs exhibit (N-1) singular (non-analytic)microscopic phase transitions of the formal order N/2, separating Nenergetically different evaporation (dissociation) states. In a suitablydesigned evaporation experiment, these types of phase transitions shouldmanifest themselves in the form of pressure and temperature oscillations,indicating cooling by evaporation. In the presence of a heat bath (thermostat),such oscillations are absent, but the canonical heat capacity shows acharacteristic peak, indicating the temperature-induced dissociation of theone-dimensional chain. The distribution of complex zeros (DOZ) of the canonicalpartition may be used to identify different degrees of dissociation in thecanonical ensemble.Comment: version accepted for publication in PRE, minor additions in the text,  references adde

physical review. e, statistical, nonlinear and soft matter physics

Nonanalytic microscopic phase transitions and temperature oscillations in the microcanonical ensemble: An exactly solvable one-dimensional model for evaporation