Related papers: Information Geometry and Chaos on Negatively Curve…
Information geometry promotes an investigation of the geometric structure of statistical manifolds, providing a series of elucidations in various areas of scientific knowledge. In the physical sciences, especially in quantum theory, this…
We present a new theoretical information-geometric framework (IGAC, Information Geometrodynamical Approach to Chaos) suitable to characterize chaotic dynamical behavior of arbitrary complex systems.
Entropic Dynamics (ED) is a theoretical framework developed to investigate the possibility that laws of physics reflect laws of inference rather than laws of nature. In this work, a RED (Reversible Entropic Dynamics) model is considered.…
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…
Information geometry is a mathematical framework that elucidates the manifold structure of the probability distribution space (p-space), providing a systematic approach to transforming probability distributions (PDs). In this study, we…
Information scrambling, the process by which quantum information spreads and becomes effectively inaccessible, is central to modern quantum statistical physics and quantum chaos. These lecture notes provide an introduction to information…
Information geometry provides a geometric approach to families of statistical models. The key geometric structures are the Fisher quadratic form and the Amari-Chentsov tensor. In statistics, the notion of sufficient statistic expresses the…
Although the notion of entropy lies at the core of statistical mechanics, it is not often used in statistical mechanical models to characterize phase transitions, a role more usually played by quantities such as various order parameters,…
The maximum entropy principle (MEP) is one of the most prominent methods to investigate and model complex systems. Despite its popularity, the standard form of the MEP can only generate Boltzmann-Gibbs distributions, which are ill-suited…
The energy level statistics of uniform random graphs are studied, by treating the graphs as random tight-binding lattices. The inherent random geometry of the graphs and their dynamical spatial dimensionality, leads to various quantum…
Our goal is to extend information geometry to situations where statistical modeling is not obvious. The setting is that of modeling experimental data. Quite often the data are not of a statistical nature. Sometimes also the model is not a…
This paper deals with the problem of identifying and estimating dynamical parameters of continuous-time quantum open systems, in the input-output formalism. First, we characterise the space of identifiable parameters for ergodic dynamics,…
We analyze the geometry of a joint distribution over a set of discrete random variables. We briefly review Shannon's entropy, conditional entropy, mutual information and conditional mutual information. We review the entropic information…
Time-independent Hamiltonian flows are viewed as geodesic flows in a curved manifold, so that the onset of chaos hinges on properties of the curvature two-form entering into the Jacobi equation. Attention focuses on ensembles of orbit…
We evaluate the information geometric complexity of entropic motion on low-dimensional Gaussian statistical manifolds in order to quantify how difficult is making macroscopic predictions about a systems in the presence of limited…
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,…
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 (ED) is a general framework for constructing indeterministic dynamical models based on entropic methods. ED has been used to derive or reconstruct both non-relativistic quantum mechanics and quantum field theory in curved…
We propose a unified theoretical framework for quantifying spatio-temporal interactions in a stochastic dynamical system based on information geometry. In the proposed framework, the degree of interactions is quantified by the divergence…
We use so-called geometrical approach in description of transition from regular motion to chaotic in Hamiltonian systems with potential energy surface that has several local minima. Distinctive feature of such systems is coexistence of…