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.
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Received 4 November 1999
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Zoido, J., Carreño, F. Geometrical entropies. The extended entropy. Eur. Phys. J. B 17, 459–469 (2000). https://doi.org/10.1007/s100510070125
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DOI: https://doi.org/10.1007/s100510070125