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Geometrical entropies. The extended entropy

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Zoido Chamorro, Jesús Manuel and Carreño Sánchez, Fernando (2000) Geometrical entropies. The extended entropy. European physical journal B, 17 (3). pp. 459-469. ISSN 1434-6028

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Official URL: http://dx.doi.org/10.1007/s100510070125



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.


Item Type:Article
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Received 4 November 1999

Uncontrolled Keywords:Geometrical entropies; Theory of measurement, Miscellaneous theories; Information science; Extended entropy; Variance
Subjects:Sciences > Physics > Optics
Sciences > Physics > Particles
Sciences > Physics > Thermodynamics
ID Code:46447
Deposited On:23 Feb 2018 13:42
Last Modified:23 Feb 2018 13:42

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