Statistical effects of distinguishable non-quantum elements

we will consider a conventional approach. Initially we will only consider non-quantum objects, i.e. for which laws of conventional mechanics suffice to deduce their properties. 

Each element lias an energy and the number of elements with this energy is The total number of elements will be N, i.e.  

The mean energy of an element is and, by applying the relation [4.2], we obtain  

The non-quantum elements composing the ensemble are distinguishable. Now, let us assume that each element only corresponds to one state, i.e. the statistical weight is equal to 1. The number of possible repartitions is the number of permutations with repetition (see Appendix 3, section A3.4.2.2) of N objects (here, elements) with wg i th3,t are similar but also 

Continuing this calculation, we will now assume that the number of elements is very high. Under these conditions, we can use Stirling s approximation [4.1] on numbers N, i, 2, etc. 

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