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A century old methodology for deriving statistical distribution using approximate Stirling’s formulation of the factorial becomes questionable. By avoiding the use of exaggerated approximations, a new picture of the energy distribution of fermions and bosons are presented. Energy distribution among fermions (or bosons) in systems with finite degeneracy are found to be degeneracy dependent. The presented point of view explains, successfully, presence of degeneracy pressure in ultra-cooled Fermi gas and predicts the minimum accessible temperature for finite degeneracy fermions system

On the Quantum Statistical Distributions Describing Finite Fermions and Bosons Systems