Canonical divergence for measuring classical and quantum complexity

A new canonical divergence is put forward for generalizing an information-geometric measure of complexity for both, classical and quantum systems. On the simplex of probability measures it is proved that the new divergence coincides with the Kullback-Leibler divergence, which is used to quantify how much a probability measure deviates from the non-interacting states that are modeled by exponential families of probabilities. On the space of positive density operators, we prove that the same divergence reduces to the quantum relative entropy, which quantifies many-party correlations of a quantum state from a Gibbs family.Comment: 17 page

The Volume of Two-Qubit States by Information Geometry

Using the information geometry approach, we determine the volume of the set of two-qubit states with maximally disordered subsystems. Particular attention is devoted to the behavior of the volume of sub-manifolds of separable and entangled states with fixed purity. We show that the usage of the classical Fisher metric on phase space probability representation of quantum states gives the same qualitative results with respect to different versions of the quantum Fisher metric

Riemannian-geometric entropy for measuring network complexity

A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a - in principle any - network a differentiable object (a Riemannian manifold) whose volume is used to define an entropy. The effectiveness of the latter to measure networks complexity is successfully proved through its capability of detecting a classical phase transition occurring in both random graphs and scale--free networks, as well as of characterizing small Exponential random graphs, Configuration Models and real networks.Comment: 15 pages, 3 figure

A geometric entropy detecting the Erd\"os-R\'enyi phase transition

We propose a method to associate a differentiable Riemannian manifold to a generic many degrees of freedom discrete system which is not described by a Hamiltonian function. Then, in analogy with classical Statistical Mechanics, we introduce an entropy as the logarithm of the volume of the manifold. The geometric entropy so defined is able to detect a paradigmatic phase transition occurring in random graphs theory: the appearance of the `giant component' according to the Erd\"os-R\'enyi theorem.Comment: 11 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1410.545

From biomechanics to learning: Continuum for the theory of physical and sports education

The structures of the human body allow biomechanical movements in a series of kinetic sequences. The study of movement is often characterized by the excessive use of new technologies that also invade dynamics with deterministic hypotheses that are only of computer engineering and only for diagnostic aspects of bioinformatics. Biomechanics is therefore often reduced to the expansion of statics and kinematics without any consideration of dynamics in the full sense of the meaning. The dynamic is the basis on which all the laws of movement are implemented, attributing a cause that includes the reaction to the stresses integrated by the decision choices of each individual person. Integration is characterized by the quality of decisions that characterize the difference between motor learning. Decisions are generated by the learning teaching processes to which every human being in developmental age is subjected. It is clear that biomechanical acquisitions can make an important contribution in the evaluation and management of problems affecting human movement, but, in an integrated way, they need other knowledge and interventions to be truly effective in their application

Por una filosofía del límite: Servio Cotta, intérprete de Montesquieu

Junto a André Masson y a Robert Shackleton, Sergio Cotta ha sido el mayor estudioso e intérprete deMontesquieu en el siglo XX. Además de haber cuidado la primera edición crítica completa del Esprit des lois (Lo spirito delle leggi, Torino, 1952), tiene elSergio Cotta, along with André Masson and Robert Shackleton, has been the most important interpreter of Montesquieu in the 20th century. Not only because he edited, although in Italian translation, the fi rst complete critical edition of the Esprit des l

Gaussian Network’s Dynamics Reflected into Geometric Entropy

We consider a geometric entropy as a measure of complexity for Gaussian networks, namely networks having Gaussian random variables sitting on vertices and their correlations as weighted links. We then show how the network dynamics described by the well-known Ornstein-Uhlenbeck process reflects into such a measure. We unveil a crossing of the entropy time behaviors between switching on and off links. Moreover, depending on the number of links switched on or off, the entropy time behavior can be non-monotonic