Maximizing Number of Reactions versus Number of Particles with Energy ei in Statistical Mechanics

Francesco R. Ruggeri
2020 Zenodo  
Traditionally, it seems statistical mechanical counting (and maximization) schemes using factorials are based on counting the number of systems in an ensemble with energy Ei or the number of particles in a system (e.g. a gas) with energy ei. In this note, we try to argue that the counting (and maximization) may be that of the number of "generalized" reactions involving a particle with ei, rather than the number of particles with ei. For Maxwell-Boltzmann statistics, the probability for ei to
more » ... ct is f(ei) (i.e. for e1 to scatter with e2, the probability is f(e1)f(e2)). Thus, the number of particles and the number of reactions involving a particle with ei are proportional. For the Fermi Dirac and Bose Einstein cases, however, this already changes. For more general cases, it seems clearer that it is the number of reactions which is related to the entropy and not configurations.
doi:10.5281/zenodo.3698243 fatcat:lw5tol2xkzdw3j4eqspth6iida