A. O. Lopes

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20242026

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math.DS2026

Ergodic Optimization and Ground States: a brief Introduction

Artur O. Lopes

Our goal in this short note is to briefly and succinctly describe some basic concepts and properties of Ergodic Optimization for readers unfamiliar with the subject. We avoid techn…

math.DS2026

A Dynamical Approach to Non-Extensive Thermodynamics

Artur O. Lopes, Paulo Varandas

We develop a non-extensive thermodynamic formalism for the one-sided shift on a finite alphabet, inspired by Tsallis' generalization of Boltzmann entropy in statistical physics. We…

math.DS2025

Nonlinear Thermodynamic Formalism: Mean-field Phase Transitions, Large Deviations and Bogoliubov's Variational Principle

Jean-Bernard Bru, Walter de Siqueira Pedra, Artur O. Lopes

Let $I^c ◯ = {1, 2, \dots, d}^{N}$ , $T$ be the shift acting on $I^c ◯$ , $P (T)$ the set of $T$ -invariant probabilities. Given a HÃ¶lder potential $A$ and a continuous fu…

math.DS2024

Directional derivatives and the central limit theorem on compact general one-dimensional lattices

Artur O. Lopes, Victor Vargas

We will show the central limit theorem for the general one-dimensional lattice where the space of symbols is a compact metric space. We consider the CLT for Lipschitz-Gibbs probabi…

math.DS2024

Idempotent approach to level-2 variational principles in Thermodynamical Formalism

A. O. Lopes, J. K. Mengue, E. R. Oliveira

In this work we introduce an idempotent pressure to level-2 functions and its associated density entropy. All this is related to idempotent pressure functions which is the natural…

math.DS2024

Parametrized Families of Gibbs Measures and their Statistical Inference

Manfred Denker, Marc KeÃebÃ¶hmer, Artur O. Lopes +1

For HÃ¶lder continuous functions $f_{i}$ , $i = 0, \dots, d$ , on a subshift of finite type and $I^ \subset R^{d}$ we consider a parametrized family of potentials $\{F_Î¸= f_0+\sum…