Nonequilibrium Fluctuations of a Brownian Particle in a Medium with Production of Entropy

The study statistically describes Brownian motion in a locally nonequilibrium medium, taking into account the production of entropy, and proposes to describe the nonequilibrium fluctuations of the velocity of a Brownian particle using a linear integro-differential equation. The characteristic functions of fluctuations of the Brownian particle velocity are obtained, which make it possible to carry out a complete statistical description of Brownian motion in a medium with the production of entropy. Findings of research show that the variance of these fluctuations increases with time according to the logarithmic law. The correlation function of fluctuations of the Brownian particle velocity is calculated and it is shown that it consists of two terms. The first term, which has a power-law dependence, describes equilibrium fluctuations, and the second, which has a logarithmic dependence, describes nonequilibrium fluctuations