  We propose a definition of phase transitions in finite systems based on
topology anomalies of the event distribution in the space of observations. This
generalizes all the definitions based on the curvature anomalies of
thermodynamical potentials and provides a natural definition of order
parameters. The proposed definition 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.
