The Fisher Information: Properties and Physico-Chemical Applications
- Authors: Jesus S. Dehesa1, Rodolfo O. Esquivel2, Angel Ricardo Plastino3, Pablo Sanchez Moreno4
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View Affiliations Hide Affiliations1 Institute “Carlos 1” for Computational and Theoretical Physics, University of Granada, Granada, Spain 2 Institute “Carlos 1” for Computational and Theoretical Physics, University of Granada, Granada, Spain 3 Institute “Carlos 1” for Computational and Theoretical Physics, University of Granada, Granada, Spain 4 Institute “Carlos 1” for Computational and Theoretical Physics, University of Granada, Granada, Spain
- Source: Concepts and Recent Advances in Generalized Information Measures and Statistics , pp 216-233
- Publication Date: December 2013
- Language: English
The Fisher Information: Properties and Physico-Chemical Applications, Page 1 of 1
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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.
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