Configuration integral

The classical configuration integral, more commonly called the partition function, andsometimes referred to as the configurational partition function [See, e.g., K. Lucas, [http://www.amazon.com/exec/obidos/ASIN/0521852404 Molecular Models for Fluids] ,Cambridge University Press, 2007( [http://books.google.com/books?id=Bxd8FlK_MBcC&pg=RA1-PA270&lpg=RA1-PA270&dq=configurational+partition+function&source=web&ots=kudgkKXsrl&sig=YAdHoZrOnXHCsGCeTulgWDwSk1s p.270, Read from Google Book] ).] ,for a system with $displaystyle\; N$particlesis defined as follows:

:where$displaystyle\; V$isthe volume enclosing the $displaystyle\; N$particles,a constant defined as: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 [Vu-Quoc, L., [http://clesm.mae.ufl.edu/wiki.pub/index.php/Configuration_integral_%28statistical_mechanics%29 Configuration integral] ,2008.] .

References