On the theory of hydrodynamic fluctuations in nonequilibrium systems

Equations are defined for the hydrodynamic nonequilibrium fluctuations in gases, and correlation properties of the fluctuations are explored. The fluctuating contributions to the pressure and heat flux are shown to be correlated in terms of the generalization of the corresponding equilibrium expressions. A fluctuating kinetic equation is used to derive the fluctuating hydrodynamic equations, which are demonstrated to be generalization of the Landau and Lifschitz equations for nonequilibrium. Equations are also presented for the one time correlation and the pair correlation function. Limiting the analysis to binary conditions and ignoring molecular chaos produced sequences of correlated binary collisions that yielded the appearance of spatial correlations. The stochastic nonequilibrium fluctuating hydrodynamic equations were identified in the general class of unsteady Gaussian Markov processes.