  We present a stability analysis of the classical ideal gas in a new theory of
nonextensive statistics and use the theory to understand the phenomena of
negative specific heat in some self-gravitating systems. The stability analysis
is made on the basis of the second variation of Tsallis entropy. It is shown
that the system is thermodynamically unstable if the nonextensive parameter is
q>5/3, which is exactly equivalent to the condition of appearance of the
negative specific heat.
