Displaying similar documents to “Voiculescu’s Entropy and Potential Theory”

Time weighted entropies

Jörg Schmeling (2000)

Colloquium Mathematicae

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For invertible transformations we introduce various notions of topological entropy. For compact invariant sets these notions are all the same and equal the usual topological entropy. We show that for non-invariant sets these notions are different. They can be used to detect the direction in time in which the system evolves to highest complexity.

Functional inequalities and uniqueness of the Gibbs measure — from log-Sobolev to Poincaré

Pierre-André Zitt (2008)

ESAIM: Probability and Statistics

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In a statistical mechanics model with unbounded spins, we prove uniqueness of the Gibbs measure under various assumptions on finite volume functional inequalities. We follow Royer's approach (Royer, 1999) and obtain uniqueness by showing convergence properties of a Glauber-Langevin dynamics. The result was known when the measures on the box [- (with free boundary conditions) satisfied the same logarithmic Sobolev inequality. We generalize this in two directions: either the constants...

Convex entropy decay via the Bochner–Bakry–Emery approach

Pietro Caputo, Paolo Dai Pra, Gustavo Posta (2009)

Annales de l'I.H.P. Probabilités et statistiques

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We develop a method, based on a Bochner-type identity, to obtain estimates on the exponential rate of decay of the relative entropy from equilibrium of Markov processes in discrete settings. When this method applies the relative entropy decays in a convex way. The method is shown to be rather powerful when applied to a class of birth and death processes. We then consider other examples, including inhomogeneous zero-range processes and Bernoulli–Laplace models. For these two models, known...

A log-Sobolev type inequality for free entropy of two projections

Fumio Hiai, Yoshimichi Ueda (2009)

Annales de l'I.H.P. Probabilités et statistiques

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We prove a kind of logarithmic Sobolev inequality claiming that the mutual free Fisher information dominates the microstate free entropy adapted to projections in the case of two projections.