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 Nparticlesis defined as follows:

:where$$displaystyle Visthe volume enclosing the $$displaystyle Nparticles,$$displaystyle etaa constant defined as:with $$displaystyle k_Bbeing the
Boltzmann constant$$displaystyle Tthe thermodynamic temperature$$displaystyle Uthe potential energy of interparticle forces, $$displaystyle { x_1 , cdots , x_N } the positions in the 3-D space $$displaystyle mathbb R ^3of the $$displaystyle Nparticles, with $$displaystyle x_i = (x_i^1 , x_i^2 , x_i^3)and$$displaystyle x_i^jthe $$displaystyle jthcoordinate of the $$displaystyle ithparticle,and$$displaystyle d^3 x_i = d x_i^1 d x_i^2 d x_i^3an 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.] .

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