Thermodynamic formalism for general iterated function systems with measures
This paper introduces a theory of Thermodynamic Formalism for Iterated Function Systems
with Measures (IFSm). We study the spectral properties of the Transfer and Markov …
with Measures (IFSm). We study the spectral properties of the Transfer and Markov …
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 …
Thermodynamic Formalism for Topological Markov Chains on Borel Standard Spaces
L Cioletti, EA Silva, M Stadlbauer - arXiv preprint arXiv:1810.03757, 2018 - arxiv.org
We develop a Thermodynamic Formalism for bounded continuous potentials defined on the
sequence space $ X\equiv E^{\mathbb {N}} $, where $ E $ is a general Borel standard …
sequence space $ X\equiv E^{\mathbb {N}} $, where $ E $ is a general Borel standard …
On information gain, Kullback-Leibler divergence, entropy production and the involution kernel
AO Lopes, JK Mengue - arXiv preprint arXiv:2003.02030, 2020 - arxiv.org
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 …
divergence, which extends the concept of Shannon entropy, plays a fundamental role. Given …
On the dimension of the space of harmonic functions on transitive shift spaces
L Cioletti, L Melo, R Ruviaro, EA Silva - Advances in Mathematics, 2021 - Elsevier
In this paper, we show a new relation between phase transition in Statistical Mechanics and
the dimension of the space of harmonic functions (SHF) for a transfer operator. This is …
the dimension of the space of harmonic functions (SHF) for a transfer operator. This is …
The double transpose of the ruelle operator
In this paper we study the double transpose of the $ L^ 1 (X,\mathscr {B}(X),\nu) $-
extensions of the Ruelle transfer operator $\mathscr {L} _ {f} $ associated to a general real …
extensions of the Ruelle transfer operator $\mathscr {L} _ {f} $ associated to a general real …
Invariant probabilities for discrete time linear dynamics via thermodynamic formalism
Invariant probabilities for discrete time linear dynamics via thermodynamic formalism* Page 1
Nonlinearity PAPER Invariant probabilities for discrete time linear dynamics via thermodynamic …
Nonlinearity PAPER Invariant probabilities for discrete time linear dynamics via thermodynamic …
Thermodynamic Formalism for Haar systems in Noncommutative Integration: transverse functions and entropy of transverse measures
AO Lopes, JK Mengue - Ergodic Theory and Dynamical Systems, 2021 - cambridge.org
We consider here a certain class of groupoids obtained via an equivalence relation (the so-
called subgroupoids of pair groupoids). We generalize to Haar systems in these groupoids …
called subgroupoids of pair groupoids). We generalize to Haar systems in these groupoids …
The Ruelle operator for symmetric -shifts
AO Lopes, V Vargas - 2020 - projecteuclid.org
Consider m∈N and β∈(1,m+1. Assume that a∈R can be represented in base β using a
development in series a=∑^∞_n=1x(n)β^-n, where the sequence x=(x(n))_n∈N takes …
development in series a=∑^∞_n=1x(n)β^-n, where the sequence x=(x(n))_n∈N takes …
Thermodynamic formalism for general IFS and quantum channels
JE Brasil - 2022 - lume.ufrgs.br
This chapter is part of [BOS22] and introduces a theory of Thermodynamic Formalism for
Iterated Function Systems with Measures (IFSm). We study the spectral properties of the …
Iterated Function Systems with Measures (IFSm). We study the spectral properties of the …