Nonextensive thermostatistics and the H theorem

The kinetic foundations of Tsallis' nonextensive thermostatistics are inves tigated through Boltzmann's transport equation approach. Our analysis follo ws from a nonextensive generalization of the "molecular chaos hypothesis." For q > 0, the q-transport equation satisfies an H theorem based on Tsallis entropy. It is also proved that the collisional equilibrium is given by Ts allis' q-nonextensive velocity distribution.