Hello Mr.O'Hara,
It is an interesting method in the respect of the laws of our themrodynamics. That said I like the principle of Pauli.
The fermions are under this law. Like for the fermi dirac statistics. If the primes are inserted for the quantum number and if the volumes of spheres considering the uniqueness are inserted with the rotations spinal and orbital. So it becomes very relevant. My theory considers this serie of uniquness , and so with its quantum serie of numbers, for the fermions but also for the bosons.
It becomes relevant when we consider the frequences of oscillations correlated with the rotating spherical volumes.see the debroglie equation with the volumes and the serie of uniqueness'universal furthermore for the two 3d scales, quant.and cosmol.
In fact that depends of what we want to interpret.In fact the pauli principle is a good tool.Now when we play with the limits, the domains, the parameters, the substitutions, settings, or superimposings or this or that, it becomes relevant when we make a kind of taxonomy.
Now of course the derivations and integrations more limits more this and that can showing the rational road.
My equations and my theory permits to see better when the groups of the uniqueness and finite and precise.The volumes from the main central sphere become very relevant and proportional with rotations and stabilities also.
The bosons are like a foto of our fermions but they turn simply in the opposite sense. The density, the mass and the volumes become so very important.If we apply the BES apllied to photons, we can with the striling approximation finding....lagrangian multipliers and we continue in a pure thermodynamical closed evolutive sphere and its central sphere, the number 1.and we have so the planck radiation equation at my knowledge.The entropy takes all its meaning in fact. Its steps of disponible energies also.
Here is an important thought. We can consider the dual system for fermions, so with their encoded bosons.(see the volumes and rotations spinal and orbital), the principle of Pauli is relevant. Now we know that two solutions are possible, 1 the fusioned system with increasing in density and correlated volumes.or 2 a binar system. In all case the system of fermions possesses both of them. But the bosons in their pure linearity, no ! The spectral energy density so is very complex and its fractalization of heat.correlated with rotating spherical volumes.
So the puzzle is not simple, that said, the pauli principle permits the good classment. In differenciating so the fermions and the bosons indeed but also the bosons encoded in these fermions !!! It is totally different about the quantum number !!!
ps the 3D is essential.....the 2 d is just for our computing ! the ferlions and bosons are purelly in 3D. now of course the convergences can be very relevant !
Best Regards