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

• Type: Article in International Scientific Journal
• Date: 2022

Authors

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

Journal

Title: Communications in Mathematical Physics

Vol. 394 No. 1

Pages: 215-256

ISSN: 0010-3616

Publisher: Springer Nature

Indexing

ISI Web of Science

Scientific classification

CORDIS: Physical sciences > Mathematics

Other information

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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 42