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  2. Partition function (statistical mechanics) - Wikipedia

    en.wikipedia.org/wiki/Partition_function...

    If the partition functions of the sub-systems are ζ 1, ζ 2, ..., ζ N, then the partition function of the entire system is the product of the individual partition functions: = =. If the sub-systems have the same physical properties, then their partition functions are equal, ζ 1 = ζ 2 = ... = ζ , in which case Z = ζ N . {\displaystyle Z ...

  3. Partition function (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Partition_function...

    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.

  4. Partition function (quantum field theory) - Wikipedia

    en.wikipedia.org/wiki/Partition_function...

    This form is closely connected to the partition function in statistical mechanics, especially since the Euclidean Lagrangian is usually bounded from below in which case it can be interpreted as an energy density. It also allows for the interpretation of the exponential factor as a statistical weight for the field configurations, with larger ...

  5. Hardy–Ramanujan–Littlewood circle method - Wikipedia

    en.wikipedia.org/wiki/Hardy–Ramanujan...

    The initial idea is usually attributed to the work of Hardy with Srinivasa Ramanujan a few years earlier, in 1916 and 1917, on the asymptotics of the partition function.It was taken up by many other researchers, including Harold Davenport and I. M. Vinogradov, who modified the formulation slightly (moving from complex analysis to exponential sums), without changing the broad lines.

  6. Maxwell–Boltzmann statistics - Wikipedia

    en.wikipedia.org/wiki/Maxwell–Boltzmann_statistics

    What has been presented above is essentially a derivation of the canonical partition function. As one can see by comparing the definitions, the Boltzmann sum over states is equal to the canonical partition function. Exactly the same approach can be used to derive Fermi–Dirac and Bose–Einstein statistics.

  7. Piecewise function - Wikipedia

    en.wikipedia.org/wiki/Piecewise_function

    Plot of the piecewise linear function = {+. In mathematics, a piecewise function (also called a piecewise-defined function, a hybrid function, or a function defined by cases) is a function whose domain is partitioned into several intervals ("subdomains") on which the function may be defined differently.

  8. Partition function (number theory) - Wikipedia

    en.wikipedia.org/wiki/Partition_function_(number...

    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.

  9. Classical XY model - Wikipedia

    en.wikipedia.org/wiki/Classical_XY_model

    The partition function can be evaluated as = {= ⁡ (+)} which can be treated as the trace of a matrix, namely a product of matrices (scalars, in this case). The trace of a matrix is simply the sum of its eigenvalues, and in the thermodynamic limit L → ∞ {\displaystyle L\to \infty } only the largest eigenvalue will survive, so the partition ...