Theory of fluctuations in a nonequilibrium gas with binary collisions

Bogolyubov's chain of equations for oiassical one-time correlation functions in a gas with binary collisions is used to obtain an equation for the long-wavelength $(ka\ll1)$ part of the binary correlation function $g_2(\mathbf p_1\mathbf r_1,\mathbf p_2\mathbf r_2,t)$ ($a$ is the radius of the interaction between the particles and $\mathbf k$ is the wave vector in the Fourier decomposition of $g_2$ as a function of $\mathbf r_1-\mathbf r_2$). This equation is inhomoganeons and the right-hand side (source) is proportional to $\delta(\mathbf r_1-\mathbf r_2)$ and is nonvanishing in a nonequilibrium state (in the absence of detailed balance in the gas). In contrast to the well-known Bogolyubov function $g_2$, which describes the correlation at distances $|\mathbf r_1-\mathbf r_2|\lesssim a$, the correlation function that is oStained describesthe correlation at distances of the order of the mean free path and greater. It does not follow adiabatically the change in time (and in space) of the first distribution function.