# 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.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## 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.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
The partition function Z is a central object in (equilibrium) statistical mechanics and one of the most important objects in these notes.
Because we want to place that result into one of our numeric ranges, the next step is to surround DateDiff with the Partition function. The syntax for the Partition function is Partition (number, start-number, stop-number, interval-number), where:
Mathieu discusses the possibility of performing exact nonperturbative computations of functional integrals related to the partition function and observables in 3D U(1) Chern-Simons theory thanks to the Deligne cohomology classes of its fiber bundles.
This paper optimizes the K-anonymity algorithm [10] known as Flexible Partition algorithm based on the rounding partition function, which regards time as an important attribute.
The partition function describes the statistical properties of the molecular system.
Although naively one may expect that other gauge symmetries, such as SO(8)4, SO(16)2, or SO(8) xSO(24), may be obtained, the modular properties of the partition function forbid the other possible extensions.
For exactly N noninteracting fermions, the partition function satisfies the recursive relation [77,78].
The regularization terms in (4.1) and (4.2) encode a prior knowledge on the local variation of the partition function, expressed as (4.4).
The partition function [c.sub.N] (n) is first studied by Chan [2] for the particular case N = 2 by considering the function [c.sub.2] (n) defined by
The entropy is a derivation of the free energy of the system, and the latter is the product of the Boltzmann constant, the temperature and the configuration partition function. The configuration partition function is a function of the total number of configuration states of the molecular chains, which is counted by a permutation and combination method known as the Flory-Huggins counting process [1, 2].
The denominator in (4) will be henceforth referred to as a partition function denoted as Z.

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