Related papers: Recent theoretical progress on an information geom…
Information geometry is the application of differential geometry in statistics, where the Fisher-Rao metric serves as the Riemannian metric on the statistical manifold, providing an intrinsic property for parameter sensitivity. In this…
We introduce a new methodology for the analysis of the phenomenon of chaotic itinerancy in a dynamical system using the notion of entropy and a clustering algorithm. We determine systems likely to experience chaotic itinerancy by means of…
A number of recent studies have estimated the inter-galactic void probability function and investigated its departure from various random models. We study a family of parametric statistical models based on gamma distributions, which do give…
Propagation of chaos for interacting particle systems has been an active research topic over decades. We propose an alternative approach to study the mean-field limit of the stochastic interacting particle systems via tools from information…
The critical behavior of quarks undergoing phase transition to hadrons is considered in the framework of the Ising model. It is found that spatial fluctuations do not alter the F-scaling result obtained earlier in the Ginzberg-Landau…
Given an arbitrary \(V \times V\) Hermitian matrix, considered as a finite discrete quantum Hamiltonian, we use methods from graph and ergodic theories to construct a \textit{quantum Poincar\'e map} at energy \(E\) and a corresponding…
We consider here a recently proposed geometrical criterion for local instability based on the geodesic deviation equation. Although such a criterion can be useful in some cases, we show here that, in general, it is neither necessary nor…
The data-driven characterization of the ``complexity'' present in dynamical systems remains an open problem with broad applications across the physical sciences. We investigate the ``structural complexity'' of the 2D ferromagnetic Ising…
The efficient detection of chaotic behavior in orbits of a complex dynamical system is an active domain of research. Several indicators have been proposed in the past, and new ones have recently been developed in view of improving the…
Information geometry is a study of statistical manifolds, that is, spaces of probability distributions from a geometric perspective. Its classical information-theoretic applications relate to statistical concepts such as Fisher information,…
Dynamical aspects of information-theoretic and entropic measures of quantum systems are studied. First, we show that for the time-dependent harmonic oscillator, as well as for the charged particle in certain time-varying electromagnetic…
Recently I proposed a simple dynamical network model for discrete space-time which self-organizes as a graph with Hausdorff dimension d_H=4. The model has a geometric quantum phase transition with disorder parameter (d_H-d_s) where d_s is…
In this work, we develop a quantum metrological framework for quantum chaos by showing that local subsystems of information scrambling systems naturally function as quantum stopwatches. The reduced quantum state of a subsystem encodes the…
We investigate signatures of quantum chaos in the mixed-field quantum Ising model on finite-size Erd\H{o}s-R\'enyi graphs using probes scalable on near-term quantum devices. By tuning the graph connectivity, the system exhibits a crossover…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
Markov Random Field models are powerful tools for the study of complex systems. However, little is known about how the interactions between the elements of such systems are encoded, especially from an information-theoretic perspective. In…
We investigate signatures of quantum chaos within Ising spin chains subjected to transverse and longitudinal fields, incorporating both local (nearest-neighbor) and non-local (long-range) couplings. While local Ising models may exhibit…
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}…
The spreading of entanglement in out-of-equilibrium quantum systems is currently at the centre of intense interdisciplinary research efforts involving communities with interests ranging from holography to quantum information. Here we…
Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior…