Hc. Eggers et U. Heinz, CRITERION FOR THE APPLICABILITY OF STANDARD THERMODYNAMICS IN HEAVY-ION COLLISIONS, Physical review. C. Nuclear physics, 48(2), 1993, pp. 530-534
The use of integrals as approximations for discrete sums in microcanon
ical 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 fireba
lls. Numerical examples with CERN and BNL parameters show that there i
s a real possibility that continuous calculations for the hadronic gas
are not accurate. By means of an example, we illustrate the dangers o
f using canonical and grand canonical methods without first testing wh
ether assumptions underlying their use are valid. Detailed investigati
ons are now required to test the difference between continuous and dis
crete calculations.