We study invariant measures for the Lorentz gas which are supported on the set of points with infinite Lyapunov exponents. We construct examples of such measures which are measures of maximal entropy and ones which are not.

This paper studies bivariate distributions with fixed marginals from an information-theoretic perspective. In particular, continuity and related properties of various information measures (Shannon entropy, conditional entropy, mutual information, Rényi entropy) on the set of all such distributions are investigated. The notion of minimum entropy coupling is introduced, and it is shown that it de...

A simple proof is given for the monotonicity of entropy and Fisher information associated to sums of i.i.d. random variables. The proof relies on a characterization of maximal correlation for partial sums due to Dembo, Kagan and Shepp.

In this paper we investigate the support of the unique measure of maximal entropy of complex Hénon maps, J∗. The main question is whether this set is the same as the analogue of the Julia set J .

We study Rényi entropy of locally excited states with considering the thermal and boundary effects respectively in two dimensional conformal field theories (CFTs). Firstly, we consider locally excited states obtained by acting primary operators on a thermal state in low temperature limit. The Rényi entropy is summation of contribution from thermal effect and local excitation. Secondly, we mainl...

Abstract We construct measures of maximal u -entropy for any partially hyperbolic diffeomorphism that factors over an Anosov torus automorphism and has mostly contracting center direction. The space such finite dimension, its extreme points are ergodic with pairwise disjoint supports.

To any periodic and full C∗–dynamical system (A, α,R) a certain invertible operator s acting on the Banach space of trace functionals of the fixed point algebra is canonically associated. KMS states correspond to positive eigenvectors of s. A Perron–Frobenius theorem asserts the existence of KMS states at inverse temperatures the logarithm of the inner and outer spectral radii of s. Such KMS st...

We study the possible Hausdorff limits of Julia sets and filled subsequences sequence dual Chebyshev polynomials a non-polar compact set $$K\subset {\mathbb C}$$ compare such to K. Moreover, we prove that measures maximal entropy for K converges weak* equilibrium measure on

Two problems: 1. whether a given family of discrete probability measures indexed by the maximal cliques of an undirected graph can be extended, and 2. how to compute explicitly the extension having maximal Shannon entropy, are examined from the point of view of graph decompositions. Close product formula for the extensions is presented and its algo-rithmical complexity is evaluated. Two conject...

Bounded weak solutions to a particular class of degenerate parabolic cross-diffusion systems are shown coincide with the unique strong solution determined by same initial condition on maximal existence interval latter. The proof relies an estimate established for relative entropy associated system.