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

The Phi-measure of event-by-event fluctuations in high-energy heavy-ion col lisions corresponds to the second moment of the fluctuating quantity distri bution of interest. It is shown that the measure based on the third moment preserves the properties of Phi but those related to the higher moments do not. In particular, only the second and third moment measures are intensive as thermodynamic quantities. The Phi(2)- and Phi(3)-measure of p(perpendic ular to)-fluctuations are computed for the hadron gas in equilibrium and th e results are analyzed in context of the experimental data. (C) 1999 Publis hed by Elsevier Science B.V, All rights reserved.