Scattering Reactions versus Configurations in Generalized Statistical Mechanics

Regular statistical mechanics makes use of the idea of configurations which are closely related to the canonical and grand canonical partition functions. In fact, in (1) a factorial counting approach is shown to lead directly to the exp(-E/T) canonical partition function weight. In a number of previous notes, we have argued one may use time reversal elastic scattering balance to obtain the Maxwell-Boltzmann (MB), Fermi-Dirac (FD) and Bose-Einstein (BE) distributions without any counting, partition functions or entropy. In (2), we tried to show how the scattering approach for the MB case may map into a counting and hence partition scheme. For generalized cases, however, with correlations between particles, we still apply the scattering approach, but it no longer seems to map to configurations. Thus, “summing” over configurations, say in a grand canonical partition, may be problematic. In this note, we try to clarify these ideas