Partition function (statistical mechanics): Difference between revisions

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= 1. </math>

This is the reason for calling ''Z'' the "partition function": it encodes how the probabilities are partitioned among the different microstates, based on their individual energies. The letter ''Z'' stands for the [[German language|German]] word ''Zustandssumme'', "sum over states". The usefulness of the partition function stems from the fact that it can be used to relate macroscopic [[thermodynamic state|thermodynamic quantities]] to the microscopic details of a system through the derivatives of its partition function. Finding the partition function is also equivalent to performing a laplace[[Laplace transform]] of the density of states function from the energy ___domain to the β ___domain, and the [[inverse laplaceLaplace transform]] of the partition function reclaims the state density function of energies.

==Grand canonical partition function==