Statistical Theory of Equilibrium Fluctuations

An analysis of the BBGKY hierarchy shows that the fluctuation theory for hydrodynamic variables (i.e., the fluid density, velocity, and temperature) must be constructed based on the hydrodynamic equations. We show that fluctuations in the hydrodynamic variables uniquely determine the fluctuations in all other thermodynamic parameters of a fluid (such as the pressure, entropy, and intrinsic energy). We find the spectral structure of fluctuation waves of the hydrodynamic variables, calculate their amplitudes, and derive the dispersion equation establishing the relation between the phase velocity of the fluctuation wave propagation and its frequency. We explain the effects of the flicker noise generation and of the stability loss on the first-order phase equilibrium lines. We also analyze the fluctuation decay process and show that this process gives rise to the effect of the Mandelstam–Brillouin scattering. We compare the obtained results with the existing fluctuation theories.