We investigate the general property of the energy fluctuation for the canonical ensemble in Tsallis statistics and the ensemble equivalence. By taking the ideal gas and the non-interacting harmonic oscillators as examples, we show that, when the part
icle number N is large enough, the relative fluctuation of the energy is proportional to 1/N in the new statistics, instead of square root of 1/N in Boltzmann-Gibbs statistics. Thus the equivalence between the microcanonical and the canonical ensemble still holds in Tsallis statistics.
We investigate the dispersion relation and Landau damping of ion acoustic waves in the collisionless magnetic-field-free plasma if it is described by the nonextensive q-distributions of Tsallis statistics. We show that the increased numbers of supert
hermal particles and low velocity particles can explain the strengthened and weakened modes of Landau damping, respectively, with the q-distribution. When the ion temperature is equal to the electron temperature, the weakly damped waves are found to be the distributions with small values of q.
