A convex analysis approach to entropy functions, variational principles and equilibrium states

• Tipo: Artigo em Revista Científica Internacional
• Data: 2022

Autores

Maria Pires de Carvalho (Autor) FCUP; Paulo Varandas (Autor) FCUP; Andrzej Bis (Autor) Outra; Miguel Ângelo de Sousa Mendes (Autor) FEUP

Revista

Título: Communications in Mathematical Physics

Vol. 394 Nº 1

Páginas: 215-256

ISSN: 0010-3616

Editora: Springer Nature

Indexação

ISI Web of Science

Classificação Científica

CORDIS: Ciências Físicas > Matemática

Outras Informações

DOI: 10.1007/s00220-022-04403-z

Abstract (EN): Using methods from Convex Analysis, for each generalized pressure function we define an upper semi-continuous affine entropy-like map, establish an abstract variational principle for both countably and finitely additive probability measures and prove that equilibrium states always exist. We show that this conceptual approach imparts a new insight on dynamical systems without a measure with maximal entropy, may be used to detect second-order phase transitions, prompts the study of finitely additive ground states for non-uniformly hyperbolic transformations and grants the existence of finitely additive Lyapunov equilibrium states for singular value potentials generated by linear cocycles over continuous self-maps.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 42