Enhancements to Fermi-Dirac and Bose-Einstein Distributions Based on Reaction Balance?

Francesco R. Ruggeri
2020 Zenodo  
In this note, we consider small enhancements to the Fermi-Dirac and Bose-Einstein distributions based on reaction balance. For fermions, reaction balance for e1+e2=e3+e4 ((1)) leads to: f(e1)[1-f(e3)] f(e2)[1-f(e4)] = f(e3)[1-f(e1)] f(e4)[1-f(e2)] ((2)) Taking ln of ((2)) and equating to ((1)) yields the Fermi-Dirac distribution. In ((2)), [1-f(e3)] represents average Pauli blocking of e1 from entering e3. [1-f(e3)] is an average value and so it seems ((2)) is an approximation. This
more » ... n. This approximation may be shown to be equivalent to that of the grand canonical partition function. If one applies reaction balance to small particle number systems (1), one may calculate more accurate Pauli blocking, it seems. We try to apply some of these ideas to the average expression ((2)) to see if a modification may be obtained. A modification is also attempted for the Bose-Einstein distribution.
doi:10.5281/zenodo.3740212 fatcat:pkcxkg6hqree3i7nuew3sixpoq