Entropy and convergence in dynamics and demography
type: Item
instance of: scholarly article
title: Entropy and convergence in dynamics and demography
zbMATH Open document ID: 0782.92014
DOI: 10.1007/BF00166145
published in: Journal of Mathematical Biology
publication date: 1993-06-29T00:00:00Z
review text: The paper starts with a review of some results by \textit{S. Goldstein} and \textit{O. Penrose} [J. Stat. Phys. 24, 325-342 (1981; Zbl 0516.70021)] on the relation between convergence rate, Kullback information, and Kolmogorov-Sinai entropy for irreducible, aperiodic finite Markov chains (including the effects of time-scaling and of coarse-graining of the state space). Elementary proofs of such results are provided. The transformation of the standard demographic Leslie projection model into a Markov chain is reviewed. An expression for the entropy in terms of the eigenvalues of the Leslie matrix is obtained. When there is a stable age distribution, the demographic meaning of the entropy is discussed in connection with the convergence rate. Finally, imprimitive and periodic limits and the relation to population entropy are discussed.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 91D20
Mathematics Subject Classification ID: 60J20
Mathematics Subject Classification ID: 60J10
zbMATH DE Number: 219779
zbMATH Keywords: demography
zbMATH Keywords: convergence rate
zbMATH Keywords: Kullback information
zbMATH Keywords: Kolmogorov-Sinai entropy
zbMATH Keywords: irreducible, aperiodic finite Markov chains
zbMATH Keywords: time-scaling
zbMATH Keywords: coarse-graining
zbMATH Keywords: demographic Leslie projection model
zbMATH Keywords: eigenvalues
zbMATH Keywords: stable age distribution
zbMATH Keywords: imprimitive and periodic limits
zbMATH Keywords: population entropy
author: Shripad D. Tuljapurkar
reviewed by: Carlos A. dos Santos Braumann
MaRDI profile type: Publication
Wikidata QID: Q52403947
cites work: The rate of convergence of a generalized stable population
cites work: On computing the entropy of the Henon attractor
cites work: Demographic Parameters and Natural Selection
cites work: Polynucleotide evolution and branching processes
cites work: Q3930348
cites work: Eigenvalue bounds on convergence to stationarity for nonreversible Markov chains, with an application to the exclusion process
cites work: Information and entropy in strange attractors
cites work: Independent coordinates for strange attractors from mutual information
cites work: Entropy increase in dynamical systems
cites work: A nonequilibrium entropy for dynamical systems
cites work: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
cites work: Q3731421
cites work: On Entropy and Generators of Measure-Preserving Transformations
cites work: Q4049307
cites work: Q4744504
cites work: Q4048871
cites work: Q3954618
cites work: Q3733844
cites work: Q4857365
cites work: Q5604742
cites work: Why use population entropy? It determines the rate of convergence
cites work: Lotka's roots under rescalings.
full work available at URL: https://doi.org/10.1007/bf00166145
OpenAlex ID: W2007585349
description: scientific article; zbMATH DE number 219779