Abstract
This chapter presents the theory of fluctuations in fluids that are in thermodynamic equilibrium. The thermal fluctuations in fluids in thermodynamic equilibrium are spatially short ranged, except when the fluid is near a critical point. Thermal fluctuations are characterized by space-time functions that account for the correlation between the value of a quantity at defined position and time with its value at defined position and time. The intensity of the fluctuations is determined by equal-time correlation functions and the dynamical properties of the fluctuations by time-dependent correlation functions. The method of fluctuating hydrodynamics for dealing with fluctuations at hydrodynamic spatiotemporal scales in fluids in thermodynamic equilibrium is presented in the chapter. It is found that in a global-equilibrium state, the values of the fluctuating fluxes have a multivariate spatiotemporal Gaussian probability distribution. The fluctuation-dissipation theorem is specified for one-component fluids and for binary fluid mixtures that obey the hydrodynamic equations. It is found that applying a double inverse Fourier transform to the static structure factor can be related to the equal-time mass density autocorrelation function.
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