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.

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 It might be outdated or ideologically biased.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.

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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.

Phase Transitions and Zeros of the Partition Function: An introduction

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:

AGE OVERDUE ACCOUNTS WITH PARTITION

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.

Nonperturbative Approaches in Field Theory

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.

A New Mining and Protection Method Based on Sensitive Data

The partition function describes the statistical properties of the molecular system.

Computational Methods for Ab Initio Molecular Dynamics

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.

Niemeier Lattices in the Free Fermionic Heterotic-String Formulation

For exactly N noninteracting fermions, the partition function satisfies the recursive relation [77,78].

Thermodynamics of Low-Dimensional Trapped Fermi Gases

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).

SPARSITY-INDUCING VARIATIONAL SHAPE PARTITIONING

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

Some Congruence Properties of a Restricted Bipartition Function [c.sub.N](n)

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].

Physically based modeling of shear modulus-temperature relationship for thermosets

The denominator in (4) will be henceforth referred to as a partition function denoted as Z.

Neuronal ensemble decoding using a dynamical maximum entropy model