Topology of event distributions as a generalized definition of phase transitions in finite systems.

We propose a definition of first order phase transitions in finite systems based on topology anomalies of the event distribution in the space of observations. This generalizes the definitions based on the curvature anomalies of thermodynamical potentials, provides a natural definition of order parameters, and can be related to the Yang-Lee theorem in the thermodynamical limit. It is directly operational from the experimental point of view. It allows to study phase transitions in Gibbs equilibria as well as in other ensembles such as the Tsallis ensemble.

Caloric curves and energy fluctuations in the microcanonical liquid-Gas phase transition

In this paper we study a microcanonical lattice gas model with a constrained average volume. We show that the caloric curve explicitly depends on the considered transformation of the volume with the excitation energy and so does not bear direct information on the characteristics of the phase transition. Conversely, partial energy fluctuations are demonstrated to be a direct measure of the equation of state. Since the heat capacity has a negative branch in the phase transition region, the presence of abnormally large kinetic energy fluctuations is a signal of the liquid-gas phase transition.