The description of the temporal evolution of some physical systems is
tackled from an information theory view-point in which Tsallis' entrop
y is extremalized with the constraints posed by the knowledge of the g
eneralized expectation values of a selected set of observables. The co
ncomitant Tsallis density operator is shown to be a particular solutio
n of von Neumann's equation and Tsallis' entropy is seen to provide on
e with a constant of the motion. The pertinent ideas are illustrated w
ith reference to the Larmor precession.