Scope of the accessibility entropy construction

The order relation in Adiabatic accessibility is a model-defined relation between equilibrium endpoints; it is not a measured trajectory law. A1–A6, A7, S1–S3, T1–T5 and C1 are adopted physical assumptions. The contact-product conclusion is conditional on the full list. In the inspected Lieb–Yngvason source, Theorem 4.8 is stated under T1–T4; the local supplier’s proof branch explicitly also needs the universal range T5 and the separate join-coherence bridge C1. The bare printed source interface does not discharge those stronger inputs.

The product representation $\tilde{S}$ is a dimensionless order parameter normalized by a chosen strict meter. A physical entropy reported in $\mathrm{J}{\mathrm{K}}^{-1}$ requires an external scale calibration and stated uncertainty. The additive constants for composition types are not fixed by the no-mixing theorem; the mixing theorem fixes only a weak monotonicity selection under its extra hypotheses.

The arbitrary-family calibration supplier assumes an explicit finite-factor representation and the Axiom of Choice for simultaneous reference/calibrator selections. The mixing supplier further requires an actual cross-type transition network, finite decorated-chain costs, A1–A6 on those transitions, and the no-sinks condition. It does not establish that arbitrary mixing or reaction channels satisfy these conditions. No-gap equality, uniqueness of reaction offsets, or strict entropy increase requires additional hypotheses and is not asserted here.

The Carathéodory treatment of Goddard is a distinct route based on local inaccessibility. It supports the conceptual distinction between accessibility assumptions and derived consequences, but it is not a second proof of the convex-contact product theorem.