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arXiv · 2601.19058

Failure of the Gibbs inequality for continuous potentials

Arantha Ranu
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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 H\"older 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.

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Arantha Ranu. 2026-01-27. Failure of the Gibbs inequality for continuous potentials. https://arxiv.org/abs/2601.19058

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