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Chaos associated with bifurcation makes a new science, but the origin and essence of chaos are not yet clear. Based on the well-known logistic map, chaos used to be regarded as intrinsic randomicity of determinate dynamics systems. However,…
The statistical mechanical description of two-dimensional inviscid fluid turbulence is reconsidered. Using this description, we make predictions about turbulent flow in a rapidly rotating laboratory annulus. Measurements on the continuously…
The central philosophy of statistical mechanics (stat-mech) and random-matrix theory of complex systems is that while individual instances are essentially intractable to simulate, the statistical properties of random ensembles obey simple…
Precision measurements with quantum systems rely on our ability to trace the differences between experimental signals to variations in unknown physical parameters. In this Letter we derive the Fisher information and the ensuing Cramer-Rao…
Dynamical processes can be transformed into graphs through a family of mappings called visibility algorithms, enabling the possibility of (i) making empirical data analysis and signal processing and (ii) characterising classes of dynamical…
The quantum Fisher information is of considerable interest not only for quantum metrology but also because it is a useful entanglement measure for finite temperature mixed states. In particular, it estimates the degree to which multipartite…
In quantum multi-parameter estimation, the precision of estimating unknown parameters is bounded by the Cramer-Rao bound (CRB), defined via the inverse of the Fisher information matrix (FIM). However, in certain scenarios such as…
A stochastic differential equation that describes the dynamics of single-domain magnetic particles at any temperature is derived using a classical formalism. The deterministic terms recover existing theory and the stochastic process takes…
We propose a novel approach to intrinsic decoherence without adding new assumptions to standard Quantum Mechanics. We generalize the Liouville equation just by requiring the dynamical semigroup property of time evolution and dropping the…
An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show that the generalized diffusion coefficient of this map has a fractal, discontinuous dependence on control parameters. An amended continuous…
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…
A discrete-time model of reacting evolving fields, transported by a bidimensional chaotic fluid flow, is studied. Our approach is based on the use of a Lagrangian scheme where {\it fluid particles} are advected by a $2d$ symplectic map…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
To make predictions or design control, information on local sensitivity of initial conditions and state-space contraction is both central, and often instrumental. However, it is not always simple to reliably determine instability fields or…
In this paper, we investigate the stochastic thermodynamics of Fisher information (FI), meaning we characterize both the \textit{fluctuations} of FI, introducing a parastatistics of that quantity, and thermodynamic quantities. We introduce…
Stickiness is a well known phenomenon in which chaotic orbits expend an expressive amount of time in specific regions of the chaotic sea. This phenomenon becomes important when dealing with area-preserving open systems because, in this…
Concepts of the complex partition functions and the Fisher zeros provide intrinsic statistical mechanisms for finite temperature and real time dynamical phase transitions. We extend the utility of these complexifications to quantum phase…
The apparantly irregular (unpredictable) space-time fluctuations in atmospheric flows ranging from climate (thousands of kilometers - years) to turbulence (millimeters - seconds) exhibit the universal symmetry of self-similarity.…
We discuss the characterization of chaotic behaviours in random maps both in terms of the Lyapunov exponent and of the spectral properties of the Perron-Frobenius operator. In particular, we study a logistic map where the control parameter…
The Fisher information matrix (FIM) plays an important role in the analysis of parameter inference and system design problems. In a number of cases, however, the statistical data distribution and its associated information matrix are either…