Entropy and convergence in dynamics and demography (Q1802939)

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.