Failure of the Gibbs inequality for continuous potentials
Abstract
It is well known that the Gibbs inequality, which says that the Gibbs ratio is bounded above and below by positive constants, holds for the unique equilibrium states of Hölder continuous potentials on shift spaces, but it can fail for continuous potentials. In this article, we study the validity of a weaker form of the Gibbs inequality in this broader setting.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
advanced mathematical theories
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 27 January 2026
- Language
- EN
- Document type
- Preprint