# Partition Function

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## partition function

[pär′tish·ən ‚fəŋk·shən] (statistical mechanics)

The integral, over the phase space of a system, of the exponential of (-

*E*/*kT*), where*E*is the energy of the system,*k*is Boltzmann's constant, and*T*is the temperature; from this function all the thermodynamic properties of the system can be derived.In quantum statistical mechanics, the sum over allowed states of the exponential of (-

*E*/*kT*). Also known as sum of states; sum over states.## Partition Function

In quantum statistical mechanics, the partition function is the inverse of the normalization factor of a Gibbs canonical distribution; other terms used in this field for the partition function are “sum of states” and “sum over states.” In classical statistical mechanics, the corresponding quantity is also known as the partition function. The partition function permits calculation of all thermodynamic potentials.