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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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Restringido a Repository staff only 298kB |

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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Additional Information: | 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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