A new form of Tsallis distribution based on the probabilistically independent postulate

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.