Entropy and probability relation with solution in statistical mechanics
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They are unrelated.
The equipartition theorem refers to individual particles and describes how energies are distributed among various degrees of freedom (translational, rotational, vibrational).
The partition function appears while computing the likelihood of finding the entire system in a specific state. It is the normalizing factor that converts populations of states with a certain energy into probabilities.
One might need to use the equipartition principle to compute the energies of specific states of the system, and this information can subsequently be fed into the partition function, but other than this, the two concepts are pretty much disjoint.
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