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Geometrical entropies. The extended entropy

  • J.M. Zoido
  • F. Carreño

Abstract:

By taking into account a geometrical interpretation of the measurement process [1, 2], we define a set of measures of uncertainty. These measures will be called geometrical entropies. The amount of information is defined by considering the metric structure in the probability space. Shannon-von Neumann entropy is a particular element of this set. We show the incompatibility between this element and the concept of variance as a measure of the statistical fluctuations. When the probability space is endowed with the generalized statistical distance proposed in reference [3], we obtain the extended entropy. This element, which belongs to the set of geometrical entropies, is fully compatible with the concept of variance. Shannon-von Neumann entropy is recovered as an approximation of the extended entropy. The behavior of both entropies is compared in the case of a particle in a square-well potential.

PACS. 03.65.Bz Foundations, theory of measurement, miscellaneous theories – 80.70.+c Information science 

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Copyright information

© EDP Sciences, Springer-Verlag, Società Italiana di Fisica 2000

Authors and Affiliations

  • J.M. Zoido
    • 1
  • F. Carreño
    • 1
  1. 1.Departamento de Optica, Escuela Universitaria de Optica, Universidad Complutense de Madrid, C/ Arcos de Jalón s/n, 28037 Madrid, SpainES

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