We derive and study quasicanonical Gibbs distribution function which is
characterized by the thermostat with finite number of particles
(quasithermostat). We show that this naturally leads to Tsallis nonextensive
statistics and thermodynamics, with Tsallis parameter q is found to be related
to the number of particles in the quasithermostat. We show that the chi-square
distribution of fluctuating temperature used recently by Beck can be partially
understood in terms of normal random momenta of particles in the
quasithermostat. Also, we discuss on the importance of the time scale hierarchy
and fluctuating probability distribution functions in understanding of Tsallis
distribution, within the framework of kinetics of dilute gas and weakly
inhomogeneous systems.Comment: 22 pages, 1 eps-figur