ON THE RELATIONSHIP BETWEEN THE FISHER-FRIEDEN-SOFFER ARROW OF TIME, AND THE BEHAVIOR OF THE BOLTZMANN AND KULLBACK ENTROPIES

We provide a new derivation of the II-theorem satisfied by Fisher's in formation measure (I) for the diffusion equation and show that the ens uing monotonically decreasing behaviour of I yields, in turn, an H-the orem involving the second time derivative of the standard Boltzmann-Gi bbs-Shannon entropy S. An upper bound for S(t) is obtained from this l atter relation. Additionally, it is demonstrated that, under certain c onditions, the behaviour of I may be related to that of the relative i nformation measure of Kullback. This latter result is generalized to t he case of the Fokker-Planck equation. (C) 1997 Elsevier Science B.V.