And temperature?

Temperature measure collision rates which are a miscount.  Collisions occur when two close particle share updates and the spin queue will exchange spin during the overlap.   So spin counts particles by cannot count overlaps so they cause direct spin exchange.

Note that Boltzman relates the Avogadro's an the N count. The Markov tree does not do collisions, the number of updates is a fixed constant at any given point in the tree.  But it is spin disequilibrium  that drives the count. hen particles are two crowded they count by twos together. There should be a even Markov solution adjacent to each odd solution.

This seems to me to be a relativity issue.  There are moments when a overlap occurs before the error generators can finish its two step adjustment reaction. Are all the N adjustments related to the finite speed of light?

Dimensionality, we have three, set the bundle of error updates to small combinations.  Light rate is set by dimensionality.  Plank and Avogadro are set by dimension because those two match on only one when the multiplicity of error terms is maximum.An Boltzxman is set from 3 analysis of collisions against a fixed Avogadro.

All of those constants must obey the Markov which tells you exactly how many updates are needed without consideration of collisions. Particle physics is about the jitter in Markov, fitting in the particle interactions which God apparently forgot.  The sidelobes, from a power spectral view, will count out the erreor patterns available as the thing jumps about in the Markov. These will be specific combinations of primes within the 3D system. 1,2,3.  It is about balancing the first and second moments on those queues.

Here is one way top think of it.  Planck tells us how many error updates are in the queue, Boltzman tells us how many have to be independent events to make the error rounded.  Matching moments in probability is the same as cancelling aliasing in power spectrum. Boltzman accopunt for particle interactions, which are not independent. A boson condensate is when Botzmann spiits the distributions to maintain the proper number of independent events.  In the 5D system two more probability moments are removed, one less than the number of queues, and the number of queues gives dimensionality. Thus the 5D system has a great many more phases of matter.