Statistics of many-particle systems

For the preliminary treatment, let us consider the simplest one-component system, e.g., thermodynamically equilibrium liquid, having a fixed number of particles. Introduce the microscopic density of a particle number defining it with the help of the Dirac -function  

Fluctuation dispersion = N — N)) ) = N ) — (N) could be expressed through mean squared of N  

As it is seen from the derivation, only the second, non-singular term 

Therefore p2 oo) = v . It is convenient to eliminate dimension-dependent concentration co-factor v , defining the joint correlation function 

Since the function emerges (in calculations) usually in a form of 

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