  The current form of Tsallis distribution for a Hamiltonian system with an
arbitrary potential is found to represent a simple isothermal situation. In
this letter, the q-exponential of a sum can be applied as the product of the
q-exponential based on the probabilistically independent postulate employed in
nonextensive statistical mechanics. Under this framework, a new form of Tsallis
distribution is suggested. It is shown that the new form of Tsallis
distribution can supply the statistical description for the nonequilibrium
dynamical property of the Hamiltonian system governed by an arbitrary
potential, and it is found to be one potential statistical distribution for the
dark matter.
