Dynamic theory of thermal fluctuations with allowance for the spatiotemporal nonlocality (Q1880166)

Previously the author showed that classical statistical mechanics for a certain class of external forces is equivalent to nonlocal hydrodynamics [Russ. Phys. J. 41, No. 3, 211--216 (2000); translation from Izv. Vyssh. Uchebn. Zaved., Fiz. 41, No. 3, 23--28 (1998)]. In the present work, formulas are derived that describe a one-to-one interrelationship between hydrodynamic nonlocality kernels and the correlation function for the thermal fluctuations of hydrodynamic quantities. This allows the spatiotemporal hydrodynamic nonlocality to be investigated in principle, for example, from spectra of molecular scattering. Analytical forms of model nonlocality kernels are discussed.