**Partition function** In statistical mechanics, the partition function Z encodes the statistical properties of a system in thermodynamic equilibrium. It is a function of temperature and other parameters, such as the volume enclosing a gas. Most of the aggregate thermodynamic variables of the system, such as the total energy, free energy, entropy, and pressure, can be expressed in terms of the partition function or its derivatives.

The partition function is a function of the temperature T and the microstate energies E1, E2, E3, etc. The microstate energies are determined by other thermodynamic variables, such as the number of particles and the volume, as well as microscopic quantities like the mass of the constituent particles. This dependence on microscopic variables is the central point of statistical mechanics. With a model of the microscopic constituents of a system, one can calculate the microstate energies, and thus the partition function, which will then allow us to calculate all the other thermodynamic properties of the system.

The canonical partition function is denoted by the letter Z (Zustandssumme; "sum over states"):

Z =

_{s=1}∑

^{N} exp(-βE

_{s}) ; exp(-βE

_{s}) is called the Bolzmann factor

β=1/k

_{B}T; β is the inverse temperature

The partition function can be related to thermodynamic properties because it has a very important statistical meaning. The probability Ps that the system occupies microstate s is

P

_{s} = (1/Z) exp(-βE

_{s})

∑

_{s} P

_{s} = 1 ; 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.

__See also__ Microstate, Macrostate

http://www.oraxcel.com/cgi-bin/yabb2/YaBB.pl?num=1296416531/0#0 __Source:__ http://en.wikipedia.org/wiki/Partition_function_%28statistical_mechanics%29