Zoido Chamorro, Jesús ManuelCarreño Sánchez, Fernando2023-06-202023-06-202000-101434-602810.1007/s100510070125https://hdl.handle.net/20.500.14352/60297Received 4 November 1999By 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.engjournal articlehttp://dx.doi.org/10.1007/s100510070125restricted access536.75535Geometrical entropiesTheory of measurementMiscellaneous theoriesInformation scienceExtended entropyVarianceÓptica (Física)PartículasTermodinámica2209.19 Óptica Física2208 Nucleónica2213 Termodinámica