Configuration integral

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 It has been suggested that this article or section be merged into Partition function (statistical mechanics). ()

The classical configuration integral, more commonly called the partition function, and sometimes referred to as the configurational partition function[1], for a system with \displaystyle N particles is defined as follows:

\displaystyle Z_N  := \int\limits_V \exp \left[ - \beta U (x_1 , \cdots , x_N) \right] d^3 x_1 \cdots d^3 x_N

(1)

where \displaystyle V is the volume enclosing the \displaystyle N particles, \displaystyle \beta a constant defined as

\displaystyle \beta  := \frac {1} {k_B T}

(2)

with \displaystyle k_B being the Boltzmann constant \displaystyle T the thermodynamic temperature \displaystyle U the potential energy of interparticle forces, \displaystyle \{ x_1 , \cdots , x_N \} the positions in the 3-D space \displaystyle \mathbb R ^3 of the \displaystyle N particles, with \displaystyle x_i = (x_i^1 , x_i^2 , x_i^3) and \displaystyle x_i^j the \displaystyle jth coordinate of the \displaystyle ith particle, and \displaystyle d^3 x_i = d x_i^1 d x_i^2 d x_i^3 an infinitesimal volume. The configuration integral has many applications from the ligand-receptor binding affinity in biochemistry to turbulence in fluid mechanics. For a detailed derivation, see the comprehensive article[2].

References

  1. ^ See, e.g., K. Lucas, Molecular Models for Fluids, Cambridge University Press, 2007 (p.270, Read from Google Book).
  2. ^ Vu-Quoc, L., Configuration integral, 2008.

Wikipedia content modification information:

  • This page was last modified on 6 September 2008, at 17:24.

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