One can certainly start from the partition function. But the partition
function is something that is additional to the microscopic
description, hence emergent. Indeed, the partition function is
different depending on whether you are using microcanonical, canonical
or grand canonical ensembles, each of which is a thermodynamic, not
microscopic concept.
I'm surprised that you consider the partition function as being "in addition" to the microscopic description. Is this the common view in statistical mechanics? Just to be specific, if I've got a system of distinguishable particles and the energy levels aren't degenerate, the single particle partition function Zsp is given by:
Zsp = sum( exp( -ei/k.T ) )
where ei is the energy of the energy level i, the sum is over all i (i.e. over all energy levels), k is the Boltzmann constant and T is the temperature.
Thanks for your patience!
Robert
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