Superstatistics of Brownian motion: A comparative study

The dynamics of temperature fluctuations of a gas of Brownian particles in local equilibrium with a nonequilibrium heat bath are described using an approach consistent with Boltzmann–Gibbs (BG) statistics. We use mesoscopic nonequilibrium thermodynamics (MNET) to derive a Fokker–Planck equation for the probability distribution in phase space including the local intensive variables fluctuations. We contract the description to obtain an effective probability distribution (EPD) from which the mass density, van Hoveʹs function and the dynamic structure factor of the system are obtained. The main result is to show that in the long time limit the EPD exhibits a similar behavior as the superstatistics distribution of nonextensive statistical mechanics (NESM), therefore implying that the coarse-graining procedure is responsible for the so-called nonextensive effects.