We focus on the dynamics of a Brownian particle whose mass fluctuates. First
we show that the behaviour is similar to that of a Brownian particle moving in
a fluctuating medium, as studied by Beck [Phys. Rev. Lett. 87 (2001) 180601].
By performing numerical simulations of the Langevin equation, we check the
theoretical predictions derived in the adiabatic limit, and study deviations
outside this limit. We compare the mass velocity distribution with truncated
Tsallis distributions [J. Stat. Phys. 52 (1988) 479] 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 behaviours. We point out a
few physical cases where the mass fluctuation problem could be encountered as a
first approximation for agglomeration- fracture non equilibrium processes.Comment: submitted to PR
