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The Fisher Information matrix is a widely used measure for applications ranging from statistical inference, information geometry, experiment design, to the study of criticality in biological systems. Yet there is no commonly accepted…
Climate is known for being characterised by strong non-linearity and chaotic behaviour. Nevertheless, few studies in climate science adopt statistical methods specifically designed for non-stationary or non-linear systems. Here we show how…
Variance and Fisher information are ingredients of the Cramer-Rao inequality. We regard Fisher information as a Riemannian metric on a quantum statistical manifold and choose monotonicity under coarse graining as the fundamental property of…
We address the following problem: given two smooth densities on a manifold, find an optimal diffeomorphism that transforms one density into the other. Our framework builds on connections between the Fisher-Rao information metric on the…
The electronic local density of states of solids, if normalized correctly, represents the probability density that the electron at a specific position has a particular energy. Because this probability density can vary in space in disordered…
We develop the characterization of the dynamics at the noise-perturbed edge of chaos in logistic maps in terms of the quantities normally used to describe glassy properties in structural glass formers. Following the recognition [Phys. Lett.…
Fisher information is a lower bound on the uncertainty in the statistical estimation of classical and quantum mechanical parameters. While some deterministic dynamical systems are not subject to random fluctuations, they do still have a…
The full family of discrete logistic maps has been widely studied both as a canonical example of the period-doubling route to chaos, and as a model of natural processes. In this paper we present a study of the stochastic process described…
We study the evolution of the probability density of ensembles of iterates of the logistic map that advance towards and finally remain at attractors of representative dynamical regimes. We consider the mirror families of superstable…
Using information theoretic quantities like the Wehrl entropy and Fisher's information measure we study the thermodynamics of the problem leading to Landau's diamagnetism, namely, a free spinless electron in a uniform magnetic field. It is…
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…
The established thermodynamic formalism of chaotic dynamics, valid at statistical equilibrium, is here generalized to systems out of equilibrium, that have yet to relax to a steady state. A relation between information, escape rate, and the…
In this work we show how the concept of majorization in continuous distributions can be employed to characterize chaotic, diffusive and quantum dynamics. The key point lies in that majorization allows to define an intuitive arrow of time,…
We theoretically investigate parameter quantum estimation in quantum chaotic systems. Our analysis is based on an effective description of non-integrable quantum systems in terms of a random matrix Hamiltonian. Based on this approach we…
We describe a compact and reliable method to calculate the Fisher information for the estimation of a dynamical parameter in a continuously measured linear Gaussian quantum system. Unlike previous methods in the literature, which involve…
Information theory is a powerful framework to capture aspects of dynamical systems with multiple degrees of freedom. Mathematically, the dynamics can be represented as a continuous curve $\mathcal{C}$ on a suitable hyperplane in flat space…
We present a thermodynamic formulation for scale-invariant systems based on the minimization with constraints of Fisher's information measure. In such a way a clear analogy between these systems's thermal properties and those of gases and…
The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this…
For a system in contact with several reservoirs $r$ at different inverse-temperatures $\beta_r$, we describe how the Markov jump dynamics with the generalized detailed balance condition can be analyzed via a statistical physics approach of…
The Fisher-Rao metric from Information Geometry is related to phase transition phenomena in classical statistical mechanics. Several studies propose to extend the use of Information Geometry to study more general phase transitions in…