20 research outputs found
Geometrical entropies. The extended entropy
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