F. Pennini et A. Plastino, FISHERS INFORMATION MEASURE IN A TSALLIS NONEXTENSIVE SETTING AND ITSAPPLICATION TO DIFFUSIVE PROCESSES, Physica. A, 247(1-4), 1997, pp. 559-569
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.