Pair Correlation Function of the Equilibrium Critical State of Fluids on a Mesoscopic Length Scale

In this paper, the "fluctuation theorem" was solved for the first time in a direct way on the mesoscopic length scale. An analytical expression was obtained for the pair correlation function of the critical state of the fluid; the parameter of the function is the density variance, which is easily reconstructed from optical experiments. Comparison of the obtained result with the Ornstein-Zernike pair correlation function made it possible to determine the Fisher correction eta = 0.25, which increases the convergence. It was shown that the obtained results provide a reliable theoretical basis for optical diagnostics of the statistical state of critical fluids.