A. Lopes

activity

19952025

most citedEntropy and Variational Principle for one-dimensional Lattice Systems with a general a-priori probability: positive and zero temperature

68 citations · 316 across the 71 of their papers we have counts for

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69 papers · 1 filter

math.DS2022

The generalized IFS Bayesian method and an associated variational principle covering the classical and dynamical cases

Artur O. Lopes, Jairo. K. Mengue

We introduce a general IFS Bayesian method for getting posterior probabilities from prior probabilities, and also a generalized Bayes' rule, which will contemplate a dynamical, as…

math.DS2022★ 1 cited

Thermodynamic Formalism on the Skorokhod space: the continuous time Ruelle operator, entropy, pressure, entropy production and expansiveness

J. Knorst, A. O. Lopes, G. Muller +1

Consider the semi-flow given by the continuous time shift $Θ_{t} : D \to D$ , $t \geq 0$ , acting on the $D$ of \textit{càdlàg} paths $w: [0,\infty) \to S…

math.DS2022

Geodesics and dynamical information projections on the manifold of Hölder equilibrium probabilities

Artur O. Lopes, Rafael O. Ruggiero

We consider here the discrete time dynamics described by a transformation $T : M \to M$ , where $T$ is either the action of shift $T = σ$ on the symbolic space $M=\{1,2,...,d\}^\mathbb{…

math.DS2021★ 3 cited

Entropy, pressure, ground states and calibrated sub-actions for linear dynamics

Artur O. Lopes, Victor Vargas

Denote by $X$ a Banach space and by $T : X \to X$ a bounded linear operator with non-trivial kernel satisfying suitable conditions. We consider the concepts of entropy - for $T$ -in…

math.DS2021★ 1 cited

Nonequilibrium in Thermodynamic Formalism: the Second Law, gases and Information Geometry

Artur O. Lopes, R. Ruggiero

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 (transf…

math.DS2020

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

Artur O. Lopes, Jairo K. Mengue

It is well known that in Information Theory and Machine Learning the Kullback-Leibler divergence, which extends the concept of Shannon entropy, plays a fundamental role. Given an {…

math.DS2019★ 3 cited

Invariant probabilities for discrete time Linear Dynamics via Thermodynamic Formalism

Artur O. Lopes, Ali Messaoudi, M. Stadlbauer +1

We show the existence of invariant ergodic $σ$ -additive probability measures with full support on $X$ for a class of linear operators $L : X \to X$ , where $L$ is a weighted shift op…

math.DS2019

Lyapunov exponents for Quantum Channels: an entropy formula and generic properties

Jader E. Brasil, Josue Knorst, Artur O. Lopes

We denote by $M_{k}$ the set of $k$ by $k$ matrices with complex entries. We consider quantum channels $ϕ_{L}$ of the form: given a measurable function $L : M_{k} \to M_{k}$ and a measure $μ$ …

math.DS2019★ 4 cited

The Ruelle operator for symmetric $β$ -shifts

Artur O. Lopes, Victor Vargas

Consider $m \in N$ and $β \in (1, m + 1]$ . Assume that $a \in R$ can be represented in base $β$ using a development in series $a = \sum_{n = 1}^{\infty} x (n) β^{- n}$ …

math.DS2019★ 6 cited

Gibbs States and Gibbsian Specifications on the space $R^{N}$

Artur O. Lopes, Victor Vargas

We are interested in the study of Gibbs and equilbrium probabilities on the lattice $R^{N}$ . Consider the unilateral full-shift defined on the non-compact set $\m…

math.DS2019

Thermodynamic Formalism for Haar systems in Noncommutative Integration: transverse functions and entropy of transverse measures

Artur O. Lopes, Jairo K. Mengue

We consider here a class of groupoids obtained via an equivalence relation (the subgroupoids of pair groupoids). We generalize to Haar Systems in these groupoids some results relat…

math.DS2019

Thermodynamic Formalism for Quantum Channels: Entropy, Pressure, Gibbs channels and generic properties

Jader E. Brasil, Josue Knorst, Artur O. Lopes

Denote $M_{k}$ the set of complex $k$ by $k$ matrices. We will analyze here quantum channels $ϕ_{L}$ of the following kind: given a measurable function $L : M_{k} \to M_{k}$ and the measure $…

math.DS2018

The sectional curvature of the infinite dimensional manifold of Hölder equilibrium prababilities

Artur O. Lopes, Rafael O. Ruggiero

Here we consider the discrete time dynamics described by a transformation $T : M \to M$ , where $T$ is the shift and $M = {1, 2, ..., d}^{N}$ . It is known that the infinite-dimens…

math.DS2018

Explicit examples in Ergodic Optimization

Hermes H. Ferreira, Artur O. Lopes, Elismar R. Oliveira

Denote by $T$ the transformation $T (x) = 2 x$ (mod 1). Given a potential $A : S^{1} \to R$ we are interested in exhibiting in several examples the explicit expression for th…

math.DS2018

An iterative process for approximating subactions

Hermes H. Ferreira, Artur O. Lopes, Elismar R. Oliveira

We describe a procedure based on the iteration of an initial function by an appropriated operator, acting on continuous functions, in order to get a fixed point. This fixed point w…

math.DS2018

Quantum Spin probabilities at positive temperature are Hölder Gibbs probabilities

Jader E. Brasil, Artur O. Lopes, Jairo K. Mengue +1

We consider the KMS state associated to the Hamiltonian $H = σ^{x} \otimes σ^{x}$ over the quantum spin lattice $C^{2} \otimes C^{2} \otimes C^{2} \otimes ...$ . For…

math.DS2018

Spectral Triples on Thermodynamic Formalism and Dixmier Trace Representations of Gibbs: theory and examples

Leandro Cioletti, L. Y. Hataishi, Artur O. Lopes +1

In this paper we study spectral triples and non-commutative expectations associated to expanding and weakly expanding maps. In order to do so, we generalize the Perron-Frobenius-Ru…

math.DS2017

Haar systems, KMS states on von Neumann algebras and $C^{*}$ -algebras on dynamically defined groupoids and Noncommutative Integration

Gilles G. de Castro, Artur O. Lopes, Gabriel Mantovani

We analyse certain Haar systems associated to groupoids obtained by certain natural equivalence relations of dynamical nature on sets like ${1, 2, ..., d}^{Z}$ , $\{1,2,...,d\…

math.DS2017

Continuous groupoids on the symbolic space, quasi-invariant probabilities for Haar systems and the Haar-Ruelle operator

Artur O. Lopes, Elismar R. Oliveira

We consider groupoids on ${1, 2, .., d}^{N}$ , cocycles and the counting measure as transverse function. We generalize results relating quasi-invariant probabilities with eige…

math.DS2017

Selection of calibrated subaction when temperature goes to zero in the discounted problem

Renato Iturriaga, Artur O. Lopes, Jairo K. Mengue

Consider $T (x) = d x$ (mod 1) acting on $S^{1}$ , a Lipschitz potential $A : S^{1} \to R$ , $0 < λ < 1$ and the unique function $b_{λ} : S^{1} \to R$ satisfying $ b_λ(x) = \max_{…

math.DS2017

The KMS Condition for the homoclinic equivalence relation and Gibbs probabilities

A. O. Lopes, G. Mantovani

D. Ruelle considered a general setting where he is able to characterize equilibrium states for Hölder potentials based on properties of conjugating homeomorphism in the so called S…

math.DS2017

Correlation Inequalities and Monotonicity Properties of the Ruelle Operator

Leandro Cioletti, Artur O. Lopes

Let $X = {1, - 1}^{N}$ be the symbolic space endowed with the product order. A Borel probability measure $μ$ over $X$ is said to satisfy the FKG inequality if for any pair o…

math.DS2017★ 2 cited

A formula for the Entropy of the Convolution of Gibbs probabilities on the circle

Artur O. Lopes

Consider the transformation $T : S^{1} \to S^{1}$ , such that $T (x) = 2 x$ (mod 1), and where $S^{1}$ is the unitary circle. Suppose $J : S^{1} \to R$ is Holder continuous and positive…

math.DS2017

A general renormalization procedure on the one-dimensional lattice and decay of correlations

Artur O. Lopes

We present a general form of Renormalization operator $R$ acting on potentials $V : {0, 1}^{N} \to R$ . We exhibit the analytical expression of the fixed po…

The generalized IFS Bayesian method and an associated variational principle covering the classical and dynamical cases

Thermodynamic Formalism on the Skorokhod space: the continuous time Ruelle operator, entropy, pressure, entropy production and expansiveness

Geodesics and dynamical information projections on the manifold of Hölder equilibrium probabilities

Entropy, pressure, ground states and calibrated sub-actions for linear dynamics

Nonequilibrium in Thermodynamic Formalism: the Second Law, gases and Information Geometry

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

Invariant probabilities for discrete time Linear Dynamics via Thermodynamic Formalism

Lyapunov exponents for Quantum Channels: an entropy formula and generic properties

The Ruelle operator for symmetric β-shifts

Gibbs States and Gibbsian Specifications on the space RN

Thermodynamic Formalism for Haar systems in Noncommutative Integration: transverse functions and entropy of transverse measures

Thermodynamic Formalism for Quantum Channels: Entropy, Pressure, Gibbs channels and generic properties

The sectional curvature of the infinite dimensional manifold of Hölder equilibrium prababilities

Explicit examples in Ergodic Optimization

An iterative process for approximating subactions

Quantum Spin probabilities at positive temperature are Hölder Gibbs probabilities

Spectral Triples on Thermodynamic Formalism and Dixmier Trace Representations of Gibbs: theory and examples

Haar systems, KMS states on von Neumann algebras and C∗-algebras on dynamically defined groupoids and Noncommutative Integration

Continuous groupoids on the symbolic space, quasi-invariant probabilities for Haar systems and the Haar-Ruelle operator

Selection of calibrated subaction when temperature goes to zero in the discounted problem

The KMS Condition for the homoclinic equivalence relation and Gibbs probabilities

Correlation Inequalities and Monotonicity Properties of the Ruelle Operator

A formula for the Entropy of the Convolution of Gibbs probabilities on the circle

A general renormalization procedure on the one-dimensional lattice and decay of correlations

The Ruelle operator for symmetric $β$ -shifts

Gibbs States and Gibbsian Specifications on the space $R^{N}$

Haar systems, KMS states on von Neumann algebras and $C^{*}$ -algebras on dynamically defined groupoids and Noncommutative Integration