Local Enhancement of Probability Due to Relaxation of Global Energy, Particle Number Constraints
Francesco R. Ruggeri · Zenodo (CERN European Organization for Nuclear Research) · 2023
In classical statistical mechanics, one often has an ideal gas of identical particles subject to the global constraints of total energy E and total number of particles N. The energy constraint prevents each particle from being completely independent because if two particles each have E/2 of the energy, the rest must have 0 energy. This not only places interdependence on the particles, but also on regions of space because one cannot consider them as independent. In the case of particle number, this also places restrictions locally because if a certain proportion of particles are in states with ej > ei, one cannot locally place as many particles as one wants into state ei. We suggest that relaxing these constraints i.e. using new constraints Sum over i ei n(ei) = Eave and Sum over i n(ei) = Nave are really approaches of enhancing local probability for e and n in e although the exact manner in which this enhancement appears must be determined. (Note: In the Fermi-Dirac case which is restrictive in n values, probability is inhibited. The enhancement is for bosons.)