Home – Home – Jornals – Journal of Structural Chemistry 2010 number 2

The paper analyzes the physical implications of the result obtained in the work [1] that a random variable - the number of the nearest neighbors M_λ in a fluid consisting of N hard spheres in the Gibbs canonical ensemble - can be expressed as a sum of N independent and similarly distributed random variables. The mean value of a functional of this random variable determines the free Helmholtz energy of a fluid with the SW interaction potential (hard sphere plus square well). The paper shows that the said property of the random variable M_λ allows one to average this functional using the general methods of the probability theory (the Cramer theorem or the method of large deviations) without expanding it in a perturbation theory series. All the mathematical variables introduced in the proof of the Cramer theorem have a simple physical meaning and are determined by the thermodynamic characteristics of the SW fluid. The conditions of the Cramer theorem are shown to hold in the entire region of the fluid existence except the critical point area.