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The partition function is a function of the temperature T and the microstate energies E 1, E 2, E 3, 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.
The partition function or configuration integral, as used in probability theory, information theory and dynamical systems, is a generalization of the definition of a partition function in statistical mechanics. It is a special case of a normalizing constant in probability theory, for the Boltzmann distribution.
A partition in which no part occurs more than once is called strict, or is said to be a partition into distinct parts. The function q(n) gives the number of these strict partitions of the given sum n. For example, q(3) = 2 because the partitions 3 and 1 + 2 are strict, while the third partition 1 + 1 + 1 of 3 has repeated parts.
Vibrational partition function, partition function for the vibrational modes of a molecule; Partition function (quantum field theory), partition function for quantum path integrals; Partition function (mathematics), generalization of the statistical mechanics concept; Partition function (number theory), the number of possible partitions of an ...
The only partition of zero is the empty sum, having no parts. The order-dependent composition 1 + 3 is the same partition as 3 + 1, and the two distinct compositions 1 + 2 + 1 and 1 + 1 + 2 represent the same partition as 2 + 1 + 1. An individual summand in a partition is called a part. The number of partitions of n is given by the partition ...
The partition function or configuration integral, as used in probability theory, information science and dynamical systems, is an abstraction of the definition of a partition function in statistical mechanics. In statistical mechanics, the partition function, Z, encodes the statistical properties of a system in thermodynamic equilibrium.
Generally, a partition is a division of a whole into non-overlapping parts. Among the kinds of partitions considered in mathematics are partition of a set or an ordered partition of a set,
(The article on unrestricted partition functions discusses this type of generating function.) For example, the coefficient of x 5 is +1 because there are two ways to split 5 into an even number of distinct parts (4 + 1 and 3 + 2), but only one way to do so for an odd number of distinct parts (the one-part partition 5).