Interactions, specifications, DLR probabilities and the Ruelle operator in the one-dimensional lattice
L Cioletti, AO Lopes - arXiv preprint arXiv:1404.3232, 2014 - arxiv.org
In this paper, we describe several different meanings for the concept of Gibbs measure on
the lattice $\mathbb {N} $ in the context of finite alphabets (or state space). We compare and …
the lattice $\mathbb {N} $ in the context of finite alphabets (or state space). We compare and …
Nonequilibrium in thermodynamic formalism: The second law, gases and information geometry
AO Lopes, R Ruggiero - Qualitative theory of dynamical systems, 2022 - Springer
In nonequilibrium thermodynamics and information theory, the relative entropy (or, KL
divergence) plays a very important role. Consider a Hölder Jacobian J and the Ruelle …
divergence) plays a very important role. Consider a Hölder Jacobian J and the Ruelle …
Correlation inequalities and monotonicity properties of the Ruelle operator
L Cioletti, AO Lopes - Stochastics and Dynamics, 2019 - World Scientific
In this paper, we provide sufficient conditions for the validity of the FKG Inequality, on
Thermodynamic Formalism setting, for a class of eigenmeasures of the dual of the Ruelle …
Thermodynamic Formalism setting, for a class of eigenmeasures of the dual of the Ruelle …
The Involution Kernel and the Dual Potential for Functions in the Walters' Family
LY Hataishi, AO Lopes - Qualitative Theory of Dynamical Systems, 2023 - Springer
First, we set a suitable notation. Points in {0, 1} Z-{0}={0, 1} N×{0, 1} N= Ω-× Ω+, are denoted
by (y| x)=(..., y 2, y 1| x 1, x 2,...), where (x 1, x 2,...)∈{0, 1} N, and (y 1, y 2,...)∈{0, 1} N. The …
by (y| x)=(..., y 2, y 1| x 1, x 2,...), where (x 1, x 2,...)∈{0, 1} N, and (y 1, y 2,...)∈{0, 1} N. The …
Semiclassical limits, Lagrangian states and coboundary equations
AO Lopes, J Mohr - Stochastics and Dynamics, 2017 - World Scientific
Assume that f is a continuous transformation f: S 1→ S 1. We consider here the cases where
f is either the transformation f (z)= z 2 or f is a smooth diffeomorphism of the circle S 1 …
f is either the transformation f (z)= z 2 or f is a smooth diffeomorphism of the circle S 1 …