Brownian particle having a fluctuating mass

We focus on the dynamics of a Brownian particle whose mass fluctuates. First we show that the behavior is similar to that of a Brownian particle moving in a fluctuating medium, as studied by Beck [Phys. Rev. Lett. 87, 180601 (2001)]. By performing numerical simulations of the Langevin equation, we check the theoretical predictions derived in the adiabatic limit, i.e. when the mass fluctuation time scale is much larger than the time for reaching the local equilibrium, and study deviations outside this limit. We compare the mass velocity distribution with truncated Tsallis distributions [J. Stat. Phys. 52, 479 (1988)] and find excellent agreement if the masses are chi-squared distributed. We also consider the diffusion of the Brownian particle by studying a Bernoulli random walk with fluctuating walk length in one dimension. We observe the time dependence of the position distribution kurtosis and find interesting behaviors. We point out a few physical cases, where the mass fluctuation problem could be encountered as a first approximation for agglomeration-fracture nonequilibrium processes.