Related papers: Statistical Complexity and Fisher-Shannon Informat…
In this work we study the helium atom confined in a spherical impenetrable cavity by using informational entropies. We use the variational method to obtain the energies and wave functions of the confined helium atom as a function of the…
In this chapter we shall discuss the recent progresses of information theoretic tools in the context of free and confined harmonic oscillator. Confined quantum systems have provided appreciable interest in areas of physics, chemistry,…
New inequalities are proved for the variance of the Pitman estimators (minimum variance equivariant estimators) of \theta constructed from samples of fixed size from populations F(x-\theta). The inequalities are closely related to the…
Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize…
Fisher Information (FI) is a quantity ubiquitously measured in such varied areas like metrology, machine learning, and biological complexity. Mathematically, it represents a lower bound in the variance of unknown parameters that are related…
Context dependence is central to the description of complexity. Keying on the pairwise definition of "set complexity" we use an information theory approach to formulate general measures of systems complexity. We examine the properties of…
We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. This allows us to calculate the complexity of phenomena for which distributions are known. We…
The notion of complexity of quantum states is quite different from uncertainty or information contents, and involves the tradeoff between its classical and quantum features. In this work, we we introduce a quantifier of complexity of…
Complexity of two-level systems, e.g. spins, qubits, magnetic moments etc, are analysed based on the so-called correlational entropy in the case of pure quantum systems and the thermal entropy in case of thermal equilibrium that are…
Motivated by the information bound for the asymptotic variance of M-estimates for scale, we define Fisher information of scale of any distribution function F on the real line as a suitable supremum. In addition, we enforce equivariance by a…
A relationship between the Fisher information and the characteristic function is established with the help of two inequalities. A necessary and sufficient condition for equality is found. These results are used to determine the asymptotic…
The subject of this paper is a mathematical transition from the Fisher information of classical statistics to the matrix formalism of quantum theory. If the monotonicity is the main requirement, then there are several quantum versions…
Diffraction on the slit can be interpreted in accordance with the Heisenberg uncertainty principle. This elementary example hints at the importance of the information theory for the quantum physics. The role played by one particularly…
We study, using information quantifiers, the dynamics generated by a special Hamiltonian that gives a detailed account of the interaction between a classical and a quantum system. The associated, very rich dynamics displays periodicity,…
Software systems are expansive, exhibiting behaviors characteristic of complex systems, such as self-organization and emergence. These systems, highlighted by advancements in Large Language Models (LLMs) and other AI applications developed…
We introduce the Fisher information in the basis of decay modes of Markovian dynamics, arguing that it encodes important information about the behavior of nonequilibrium systems. In particular we generalize an orthonormality relation…
We show that the mathematical form of the information measure of Fisher's I for a Gibbs' canonical probability distribution (the most important one in statistical mechanics) incorporates important features of the intrinsic structure of…
Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to a…
In a classical measurement the Shannon information is a natural measure of our ignorance about properties of a system. There, observation removes that ignorance in revealing properties of the system which can be considered to preexist prior…
We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…