Infinite Statistics and the Gross Pitaevskii Equation

We clarify that an ideal gas obeying infinite statistics cannot undergo condensation. Then we derive the dynamic equation for an identical particle system obeying infinite statistics under external potential and inter-particle interaction. The derivation utilizes the Hamiltonian written in terms of the number operators and the transition number operators. At a very low temperature, where one can discard the dynamics of the excited occupation level, the dynamic of an infinite statistics system can be described by the Gross Pitaevskii equation, similar to the Bose-Einstein case.