open_problem: ax-2607.07851-51bcfa22

This data as json

id statement domain sourced_how source_url cheapest_test status claimed_by sourced_by shape created_ts updated_ts
ax-2607.07851-51bcfa22 Problem 4.9 (Entropy-only rigidity): Theorem 4.1 assumed entropy invariance for all states. Determine the minimal state classes $\mathcal{F}$ for which “ $\mathsf{S}[f_{*}\rho]=\mathsf{S}[\rho]$ for all $\rho\in\mathcal{F}$ ” still forces $J_{f}\equiv 1$ (e.g., Gaussians only; kime states with von Mises phase laws only), and, dually, characterize the group of transformations preserving the entropy of every equilibrium (phase-equipartitioned) kime state. The latter group is strictly larger than the measure-preserving group (it contains all fiberwise rotations $\theta\mapsto\theta+c(J)$ trivially, but also non-measure-preserving maps acting only on null sets of equilibria); its computation quantifies exactly how much of the symplectic structure is visible to equilibrium thermodynamics alone. mathematical physics / math-ph enumerated in arXiv paper titled 'open problems' (formal problem environment): Kime-Representation Formulations of Three Open Problems in the Foundations of Classical Mechanics: Uncertainty, Invarian https://arxiv.org/abs/2607.07851   open   ts-synth unclassified 2026-09-02T17:57:21Z 2026-09-02T17:57:21Z

Links from other tables