Generalizing Φ-measure of event-by-event fluctuations in high-energy heavy-ion collisions

The Φ-measure of event-by-event fluctuations in high-energy heavy-ion collisions corresponds to the second moment of the fluctuating quantity distribution of interest. It is shown that the measure based on the third moment preserves the properties of Φ but those related to the higher moments do not. In particular, only the second and third moment measures are intensive as thermodynamic quantities. The Φ2- and Φ3-measure of p⊥-fluctuations are computed for the hadron gas in equilibrium and the results are analyzed in context of the experimental data.