Related papers: Information geometric complexity of entropic motio…
It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can…
Information geometric techniques and inductive inference methods hold great promise for solving computational problems of interest in classical and quantum physics, especially with regard to complexity characterization of dynamical systems…
Information geometry and inductive inference methods can be used to model dynamical systems in terms of their probabilistic description on curved statistical manifolds. In this article, we present a formal conceptual reexamination of the…
We investigate the effect of different metrizations of probability spaces on the information geometric complexity of entropic motion on curved statistical manifolds. Specifically, we provide a comparative analysis based upon Riemannian…
We study the information geometry and the entropic dynamics of a 3D Gaussian statistical model. We then compare our analysis to that of a 2D Gaussian statistical model obtained from the higher-dimensional model via introduction of an…
Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and,…
Motivated by the presence of deep connections among dynamical equations, experimental data, physical systems, and statistical modeling, we report on a series of findings uncovered by the Authors and collaborators during the last decade…
We characterize the complexity of geodesic paths on a curved statistical manifold M_{s} through the asymptotic computation of the information geometric complexity V_{M_{s}} and the Jacobi vector field intensity J_{M_{s}}. The manifold M_{s}…
We compute the asymptotic temporal behavior of the dynamical complexity associated with the maximum probability trajectories on Gaussian statistical manifolds in presence of correlations between the variables labeling the macrostates of the…
The behavior of any physical system is governed by its underlying dynamical equations. Much of physics is concerned with discovering these dynamical equations and understanding their consequences. In this work, we show that, remarkably,…
Can the spatial distance between two identical particles be explained in terms of the extent that one can be distinguished from the other? Is the geometry of space a macroscopic manifestation of an underlying microscopic statistical…
Newtonian dynamics is derived from prior information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the state of a particle is defined by…
Entropic dynamics is a framework in which the laws of dynamics are derived as an application of entropic methods of inference. Its successes include the derivation of quantum mechanics and quantum field theory from probabilistic principles.…
We consider a Gaussian statistical model whose parameter space is given by the variances of random variables. Underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as…
We present an extension of the ergodic, mixing, and Bernoulli levels of the ergodic hierarchy for statistical models on curved manifolds, making use of elements of the information geometry. This extension focuses on the notion of…
Entropic dynamics is a framework for defining dynamical systems that is aligned with the principles of information theory. In an entropic dynamics model for motion on a statistical manifold, we find that the rate of changes for expected…
We propose to examine the predictability and the complexity characteristics of the Standard&Poor500 dynamics behaviors in a coarse-grained way using the symbolic dynamics method and under the prism of the Information theory through the…
We discuss here the use of generalized forms of entropy, taken as information measures, to characterize phase transitions and critical behavior in thermodynamic systems. Our study is based on geometric considerations pertaining to the space…
Experimental sciences have come to depend heavily on our ability to organize and interpret high-dimensional datasets. Natural laws, conservation principles, and inter-dependencies among observed variables yield geometric structure, with…
In this paper we study two entropic dynamical models from the viewpoint of information geometry. We study the geometry structures of the associated statistical manifolds. In order to analyse the character of the instability of the systems,…