The R\'enyi entropies of quasiparticle excitations in the many-body gapped systems show a remarkable universal picture which can be understood partially by combination semiclassical argument with quantum effect (in)distinguishability. are independent model, momenta, and connectedness subsystem. In this letter we calculate exactly single-interval double-interval fermions, bosons, XY chains. We f...

We investigate classical and quantum geometric information flow theories (GIFs QGIFs) when the evolution field equations for nonholonomic Einstein systems, NES, are derived from Perelman–Lyapunov-type entropic-type functionals. The term NES encodes models fundamental physical subjected to (equivalently, nonintegrable, anholonomic) constraints. There used canonical variables that allow a general...

We show that Tsallis’ distributions can be derived from the standard (Shannon) maximum entropy setting, by incorporating a constraint on the divergence between the distribution and another distribution imagined as its tail. In this setting, we find an underlying entropy which is the Rényi entropy. Furthermore, escort distributions and generalized means appear as a direct consequence of the cons...

In recent years, there has been a growing interest in considering the quantitative aspects of Information Flow, partly because often the a priori knowledge of the secret information can be represented by a probability distribution, and partly because the mechanisms to protect the information may use randomization to obfuscate the relation between the secrets and the observables. Several works i...

Abstract: Mixture models are in high demand for machine-learning analysis due to their computational tractability, and because they serve as a good approximation for continuous densities. Predominantly, entropy applications have been developed in the context of a mixture of normal densities. In this paper, we consider a novel class of skew-normal mixture models, whose components capture skewnes...

Escort distributions are a simple one parameter deformation of an original distribution p. In Tsallis extended thermostatistics, the escort-averages, defined with respect to an escort distribution, have revealed useful in order to obtain analytical results and variational equations, with in particular the equilibrium distributions obtained as maxima of Rényi-Tsallis entropy subject to constrain...