On information gain, Kullback-Leibler divergence, entropy production and the involution kernel

DOI10.3934/dcds.2022026OpenAlexW3009523046MaRDI QIDQ2144305

Jairo K. Mengue, Artur Oscar Lopes

Publication date: 1 June 2022

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.02030

zbMATH Keywords

entropypressurethermodynamic formalismentropy productionKullback-Leibler divergenceinformation gainsymbolic spaces

Mathematics Subject Classification ID

Stationary stochastic processes (60G10) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Measures of information, entropy (94A17) Information theory (general) (94A15) Statistical aspects of information-theoretic topics (62B10)

Related Items (4)

Decision theory and large deviations for dynamical hypotheses tests: the Neyman-Pearson lemma, min-max and Bayesian tests ⋮ Nonequilibrium in thermodynamic formalism: the second law, gases and information geometry ⋮ Haar systems, KMS states on von Neumann algebras and \(C^*\)-algebras on dynamically defined groupoids and noncommutative integration ⋮ The involution kernel and the dual potential for functions in the Walters' family

Cites Work

• A Mathematical Theory of Communication
• A generalized detailed balance relation
• Gibbs measures and phase transitions.
• Entropy, pressure and duality for Gibbs plans in ergodic transport
• Relative entropy and identification of Gibbs measures in dynamical systems
• The fluctuation theorem as a Gibbs property
• The zeta function, non-differentiability of pressure, and the critical exponent of transition
• On the dimension of the space of harmonic functions on transitive shift spaces
• Nonequilibrium in thermodynamic formalism: the second law, gases and information geometry
• Product type potential on the one-dimensional lattice systems: selection of maximizing probability and a large deviation principle
• On entropy production of repeated quantum measurements. I. General theory
• Phase transitions in one-dimensional translation invariant systems: a Ruelle operator approach
• Lyapunov minimizing measures for expanding maps of the circle
• Exact bounds for the polynomial decay of correlation, 1/fnoise and the CLT for the equilibrium state of a non-Hölder potential
• Entropy and variational principle for one-dimensional lattice systems with a generala prioriprobability: positive and zero temperature
• Duality results for iterated function systems with a general family of branches
• Foundations of Ergodic Theory
• A natural space of functions for the Ruelle operator theorem
• Examples for the Nonuniqueness of the Equilibrium State
• Large deviations for quantum spin probabilities at temperature zero
• A variational principle for the specific entropy for symbolic systems with uncountable alphabets
• Thermodynamic formalism for Haar systems in noncommutative integration: transverse functions and entropy of transverse measures
• Correlation inequalities and monotonicity properties of the Ruelle operator
• Spectral properties of the Ruelle operator for product-type potentials on shift spaces
• A LARGE DEVIATION PRINCIPLE FOR THE EQUILIBRIUM STATES OF HÖLDER POTENTIALS: THE ZERO TEMPERATURE CASE
• Elements of Information Theory
• On Information and Sufficiency
• Entropy production and information gain in axiom-A systems
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