  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 particle 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.
