Features of the Extension of a Statistical Measure of Complexity to Continuous Systems

Abstract

We discuss some aspects of the extension to continuous systems of a statistical measure of complexity introduced by Lopez-Ruiz, Mancini and Calbet (LMC) [Phys. Lett. A 209 (1995) 321]. In general, the extension of a magnitude from the discrete to the continuous case is not a trivial process and requires some choice. In the present study, several possibilities appear available. One of them is examined in detail. Some interesting properties desirable for any magnitude of complexity are discovered on this particular extension.

22 pages, 0 figures

References in corpus (2)

• A Statistical Measure of Complexity
• Tendency to Maximum Complexity in a Non-Equilibrium Isolated System

Cited by in corpus (69)

• New definition of complexity for self-gravitating fluid distributions: The spherically symmetric, static case
• Definition of complexity for dynamical spherically symmetric dissipative self-gravitating fluid distributions
• Statistical complexity, Fisher-Shannon information, and Bohr orbits in the H-atom
• Complexity Factor for Charged Spherical System
• $f(\mathcal{G},T_{\alpha \beta }{T}^{\alpha \beta })$ Theory and Complex Cosmological Structure
• Influence of Modification of Gravity on the Complexity Factor of Static Spherical Structures
• Complexity Factor For Static Anisotropic Self-Gravitating Source in $f(R)$ Gravity
• Complexity and neutron stars structure
• New Definition of Complexity Factor in $f(R,T,R_{\mu \nu }{T}^{\mu \nu })$ Gravity
• A Generalized Statistical Complexity Measure: Applications to Quantum Systems
• Monotone measures of statistical complexity
• Uncharged and charged anisotropic like--Durgapal stellar model with vanishing complexity
• The Measure of Complexity in Charged Celestial Bodies in $f(R,T,R_{\mu \nu }{T}^{\mu \nu })$ Gravity
• Gravitational cracking and complexity in the framework of gravitational decoupling
• Complexity Factor For Anisotropic Source in Non-minimal Coupling Metric $f(R)$ Gravity
• Comparison of SDL and LMC measures of complexity: Atoms as a testbed
• Role of gravitational decoupling on isotropization and complexity of self-gravitating system under complete geometric deformation approach
• Information entropy and complexity measure in generalized Kratzer potential
• Complexity Factor for Static Sphere in Self-interacting Brans-Dicke Gravity
• Two-dimensional confined hydrogen: An entropy and complexity approach
• Configuration Complexities of Hydrogenic Atoms
• Differential entropy and time
• Measure of Complexity in Self-Gravitating Systems using Structure Scalars
• Some features of the statistical complexity, Fisher-Shannon information, and Bohr-like orbits in the Quantum Isotropic Harmonic Oscillator
• Complexity of Dynamical Dissipative Cylindrical System in Non-minimally Coupled Theory
• Various complexity measures in confined hydrogen atom
• Scaling properties of composite information measures and shape complexity for hydrogenic atoms in parallel magnetic and electric fields
• Complexity of D-dimensional hydrogenic systems in position and momentum spaces
• Quantum information measures of the Aharonov-Bohm ring in uniform magnetic fields
• Alternative evaluation of statistical indicators in atoms: the non-relativistic and relativistic cases
• Complexity measures and uncertainty relations of the high-dimensional harmonic and hydrogenic systems
• Information-theoretic measures for a position-dependent mass system in an infinite potential well
• Entropy and complexity analysis of hydrogenic Rydberg atoms
• Complexity factor of spherically anisotropic polytropes from gravitational decoupling
• Complexity factor for black holes in the framework of the Newman-Penrose formalism
• Gravitational Cracking of General Relativistic Polytropes: a generalized scheme
• Theory of the Robin quantum wall in a linear potential. I. Energy spectrum, polarization and quantum-information measures
• Dynamics of order-disorder and complexity for interacting bosons in optical lattice
• Comparative analysis of information measures of the Dirichlet and Neumann two-dimensional quantum dots
• Quantum Tunneling and Information Entropy in a Double Square Well Potential: Ammonia Molecule
• Calculation of statistical entropic measures in a model of solids
• Renyi entropy of the infinite well potential in momentum space and Dirichlet-like trigonometric functionals
• Information entropy for a two-dimensional rotating Bose-Einstein condensate
• Comparison of information criteria for detection of useful signal in noisy environment
• One-parameter Fisher-Rényi complexity: Notion and hydrogenic applications
• Statistical measure of complexity for quantum systems with continuous variables
• Entropy and complexity analysis of the D-dimensional rigid rotator and hyperspherical harmonics
• Statistical measures and the Klein tunneling in single-layer graphene
• Quantum information measures of the one-dimensional Robin quantum well
• Entropy and complexity properties of the d-dimensional blackbody radiation
• Differential-escort transformations and the monotonicity of the LMC-Rényi complexity measure
• Information and Complexity Analysis of Spatial Data
• Quantum information measures of the Dirichlet and Neumann hyperspherical dots
• The biparametric Fisher-Rényi complexity measure and its application to the multidimensional blackbody radiation
• Biparametric complexities and the generalized Planck radiation law
• Complexity analysis of hypergeometric orthogonal polynomials
• Complexity-like properties and parameter asymptotics of ${\mathfrak{L}}_q$-norms of Laguerre and Gegenbauer polynomials
• Study of Complexity Factor and Stability of Dynamical Systems in $f(G)$ Gravity
• Complexity of Charged Dynamical Spherical System in Modified Gravity
• Study of a quantum scattering process by means of entropic measures
• Quantum-information theory of a Dirichlet ring with Aharonov-Bohm field
• Statistical measure of complexity and correlated behavior of Fermi systems
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions
• London superconductivity approach in a time-dependent background
• A Complexity-Based Approach to Quantum Observable Equilibration
• Heisenberg uncertainty relation and statistical measures in the square well
• Complexity of multidimensional hydrogenic systems
• Statistical complexity as a probe of mass and phase structure in compact objects
• Information analysis in free and confined harmonic oscillator