Uniqueness of Equilibrium States for Lorenz Attractors in Any Dimension

Maria Jose Pacifico, Fan Yang, Jiagang Yang

correcthigh confidence

Category: Not specified
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper establishes uniqueness via a fixed-scale Climenhaga–Thompson criterion by verifying (i) almost expansivity (proven at a specific scale in their companion work), (ii) tail weak specification and a Bowen property on a good orbit-core using Liao’s scaled linear Poincaré flow, and (iii) a pressure gap for bad/prefix/suffix pieces; this is clearly stated and structured around Theorems 2.1, 3.1, 3.3, and 3.4 and Theorem A for Lorenz attractors in any dimension. The candidate’s outline mirrors the paper but incorrectly claims that entropy expansivity implies almost expansivity (the paper uses a separate result to obtain almost expansivity) and gives an imprecise pressure-gap bound. Hence the model’s proof has critical gaps while the paper’s argument is correct.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The paper delivers a concise and effective proof of uniqueness of equilibrium states for Hölder potentials on Lorenz attractors in any dimension for an open-dense set of vector fields. It combines a fixed-scale specification criterion with robust Lorenz-class topology and Liao’s scaled linear Poincaré flow. The arguments appear correct and well-targeted. Minor clarifications would improve self-containment, especially regarding the source and statement of almost expansivity and the modified variational principle used for the pressure gap.