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 η = 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.