Criterion for the applicability of standard thermodynamics in heavy ion collisions

The use of integrals as approximations for discrete sums in microcanonical equilibrium calculations is valid in the thermodynamic limit. We derive a criterion for testing the validity of this approximation for the relatively small volumes encountered in heavy ion collision fireballs. Numerical examples with CERN and BNL parameters show that there is a real possibility that continuous calculations for the hadronic gas are not accurate. By means of an example, we illustrate the dangers of using canonical and grand canonical methods without first testing whether assumptions underlying their use are valid. Detailed investigations are now required to test the difference between continuous and discrete calculations.