EQUILIBRIUM STATES BY SYNCHRONIZATION, SYMBOLIC EXTENSIONS, AND FACTORS

Katrin Gelfert, Dominik Kwietniak, Yuri Lima

correctmedium confidence

Category: math.DS
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper’s Theorem B proves that, for continuous fixed-point-free flows, choosing the time-change r(y)=Ptop(Φ,f)−(1/T)∫_0^T f(ϕ_s(y))ds>0 transforms equilibrium states for f into measures of maximal entropy for the time-changed flow Φ_r, with uniqueness preserved. The proof uses the invariant-measure bijection under time-change, Abramov’s entropy scaling, and the pressure variational principle. The candidate solution follows the same structure and correctly flags a notational glitch in the paper’s statement (1.2), where a “max_y” appears; the body of the paper and its proof clearly use the pointwise r(y). Aside from this typographical issue, the arguments match and are correct.

Referee report (LaTeX)

\textbf{Recommendation:} minor revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The result is correct and the proof is clean, conceptually leveraging synchronization via time change to translate equilibrium-state questions into MME questions. The approach is broadly useful and coheres with known techniques (Parry-style synchronization, Abramov scaling). The only requested changes are to fix a notational glitch (the definition of r in (1.2)) and to make some clarifying remarks explicit for readability.