%0 Journal Article
%A Zoido Chamorro, Jesús Manuel
%A Carreño Sánchez, Fernando
%T Geometrical entropies. The extended entropy
%D 2000
%@ 1434-6028
%U https://hdl.handle.net/20.500.14352/60297
%X 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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