FISHERS INFORMATION MEASURE IN A TSALLIS NONEXTENSIVE SETTING AND ITSAPPLICATION TO DIFFUSIVE PROCESSES

Fisher's information measures, as adapted to a nonextensive (Tsallis) environment, are discussed. For systems of particles that are in a gen eral state of motion a lower bound to these information measures is de rived with the help of a recently established upper bound to the entro py increase. This lower bound to the information measure is the basis for a variational principle devised to determine unknown probability d istributions. In the important instance of diffussion processes we sho w that trying to ascertain which is the probability distribution that maximizes Fisher's information sheds some light on the meaning of Tsal lis' q-parameter. We discuss applications to cosmological models that seem to suggest that a non-extensive thermostatistics with g = -1 prov ides an adequate scenario for discussing gravitation.