The Fisher Information: Properties and Physico-Chemical Applications
Pp. 216-233 (18)
Jesus S. Dehesa, Rodolfo O. Esquivel, Angel Ricardo Plastino and Pablo Sanchez-Moreno
The Fisher information functional occupies a very special position among the uncertainty
measures of quantum systems of any dimensionality. In contrast with (global)
entropic measures of Shannon, Renyi or Tsallis types, it contitutes a local measure in
the sense that it is sensitive to the oscillatory character of the probability density distribution.
Moreover, the Fisher information is closely related to various macroscopic
properties of the system described by different density functionals. Here, we review its
main analytical properties such as, inequality-based relationships with some radial expectation
values and its uncertainty relation. Tighter versions of these inequalities are
shown for those systems subject to an arbitrary central potential. Moreover, the Fisher
information is computed for D-dimensional hydrogenic systems explicitly in terms of
the radial and angular hyperquantum numbers characterizing the quantum states of
the system in both position and momentum spaces. Finally, the utility of this quantity
is discussed for various physico-chemical processes of recent interest: Abstraction and
nucleophilic substitution reactions.
Information theory, Fisher information, D-dimensional hydrogenic systems,
chemical reactions, abstraction and nucleophilic substitution reactions.
Institute “Carlos 1” for Computational and Theoretical Physics, University of Granada, Granada, Spain