On the Statistics of an Ideal Gas with Mass Fluctuations and the Boltzman Ergodic Theorem: The Combined Boltzman–Tsallis Statistics

Abstract

In this letter, we evaluate the effective velocities probability distribution associated to a classical ideal gas in thermodynamical equilibrium, but in the presence of fluctuations of the (inertial) mass parameter of the molecules. We obtain in the context of linear response theory of the mass fluctuations and the usual Boltzman framework the combined statistics of Boltzman and Tsallis as an outcome of the study for our effective Fractal gas distribution probability. This result explains from first principles the Tsallis-inverse power law distribution previously only speculated on in the literature. Finally, we give a new mathematical proof of the Boltzman ergodic theorem in classical statistics mechanics.