Nonextensive Thermostatistics and theHTheorem

The kinetic foundations of Tsallis' nonextensive thermostatistics are investigated through Boltzmann's transport equation approach. Our analysis follows from a nonextensive generalization of the “molecular chaos hypothesis.” For $q>\mathrm{}0\mathrm{}$, the $q$-transport equation satisfies an $H$ theorem based on Tsallis entropy. It is also proved that the collisional equilibrium is given by Tsallis' $q$-nonextensive velocity distribution.