Layered Irreversible Accessibility and Model-Space Entropic Tomography in Degenerate Compact Matter

Conceptual origin and scope This work originated from a broader question concerning the physical basis of irreversible progression: If temporal progression is physically recorded through irreversible changes, is the relevant rate determined by the speed of microscopic motion, or by the availability of pathways through which persistent, distinguishable changes can occur? The question becomes especially interesting in extremely dense matter. Such matter may contain intense microscopic motion, rapid interactions, collective modes, and highly organized structures while simultaneously restricting many possible state transitions through Pauli blocking, pairing gaps, kinematic thresholds, and other constraints. The central distinction motivating this work is therefore: microscopic activity --> irreversible accessibility --> operational record of progression The manuscript uses irreversible accessibility to denote the availability of physical pathways through which a subsystem can undergo changes that are distinguishable and not reversed on the timescale of interest. The purpose is not to claim that microscopic motion disappears in degenerate matter, nor to identify low dissipative activity with stopped time. Rather, the aim is to explore whether a highly active physical system can contain spatially localized regions in which irreversible differentiation is comparatively easy, difficult, suppressed, or redirected. Relation to the Dragon’s Egg thought experiment One motivating thought experiment concerns the hypothetical inhabitants of a neutron-star surface described in Robert Forward’s novel Dragon’s Egg. A natural first intuition might be that such entities would experience time extremely rapidly because their proposed nuclear-matter chemistry would involve much faster microscopic processes than ordinary terrestrial chemistry. The present work arose partly from questioning that inference. Fast microscopic kinetics do not necessarily imply a proportionally fast rate of meaningful irreversible progression. An operational clock, biological system, or record-forming subsystem would require not only rapid motion or reaction, but also accessible pathways that generate persistent and distinguishable changes. The motivating possibility can therefore be expressed as: fast microscopic kinetics --> fast irreversible record formation Conversely, low dissipative accessibility --> absence of microscopic activity This manuscript does not attempt to calculate subjective time, biological time, or the temporal experience of hypothetical neutron-star organisms. The thought experiment serves only as a conceptual motivation for examining irreversible accessibility separately from raw microscopic activity. What the paper actually develops The numerical model is deliberately prescribed and non-microscopic. It does not attempt to calculate a realistic neutron-star interior. Instead, it constructs a sequence of transparent diagnostic layers: Fermi thermal sensitivity --> radial shell activity --> pairing-induced suppression --> --> composition thresholding --> propagation comparison --> projected angular structure These layers are represented by toy prescriptions for: an integrated Fermi–Dirac thermal-window diagnostic; shell-weighted emissivity-like activity; a localized isotropic pairing mask; a prescribed direct-Urca accessibility threshold; an independently imposed matter-sensitive propagation marker; a projected shell-weighted emissivity proxy. The individual quantities are not assumed to be the same physical observable. They form a hierarchy of model-space diagnostics rather than a single universal accessibility scalar. The paper therefore distinguishes: thermodynamic entropy production --> channel activity or entropy export --> --> operational irreversible-time calibration The notation \kappa_{\rm op} is used only in the last of these layers. It denotes an operational calibration between a selected irreversible activity record and proper time. It is not proposed as a universal material constant, transport coefficient, or replacement for physical time. Meaning of “entropic tomography” The term model-space entropic tomography is used in a restricted and non-observational sense. It does not denote: an observational reconstruction of a neutron-star interior; a neutrino-tomography method; a measurement of entropy density; a demonstrated inversion from surface data; a direct map of subjective or experienced time. Instead, it refers to the structured mapping of model-defined fields indicating where irreversible pathways are open, restricted, suppressed, or redirected. The diagnostic question is therefore not simply: What matter is present? It is: Under the imposed model conditions, where are irreversible pathways open, restricted, or redirected, and which mechanisms produce that pattern? Status of the physical model The calculations are intended as a proof of concept for a phenomenological diagnostic framework. They are not a neutron-star cooling model, equation-of-state calculation, microscopic pairing calculation, neutrino-radiation-transport solution, or general-relativistic transfer calculation. In particular, the model does not: solve the Tolman–Oppenheimer–Volkoff equations; derive a self-consistent equation of state; calculate beta-equilibrated composition; evaluate complete reaction collision integrals; derive direct-Urca activation from microscopic composition; calculate realistic pairing gaps; use universal superfluid reduction factors; solve neutrino transport; calculate microscopic coherence or phase stiffness; infer operational time directly from neutrino emissivity. The prescribed fields are therefore not predictions of a real neutron star. They are controlled mathematical objects used to demonstrate how layered irreversible-accessibility diagnostics can be constructed and compared. Broader research context This paper was developed independently as a phenomenological layer within a broader investigation of irreversibility, operational progression, and possible microscopic descriptions of local state transformation. The present Zenodo record intentionally does not depend on, and does not claim to validate, any particular microscopic ontology. In particular, it should not be interpreted as a derivation from a microscopic algebra, a confirmation of an emergent-geometry program, or evidence that a deeper theoretical framework has succeeded. A future microscopic theory may attempt to derive transport, irreversible accessibility, or effective coarse-grained geometry from local state transformations. If such a theory becomes sufficiently developed, the diagnostics introduced here could serve as possible comparison targets. At present, however, the paper remains deliberately agnostic about whether such a derivation exists. Why the work is being shared The manuscript is being deposited as an openly accessible exploratory research object so that: the conceptual framework can be documented; the toy prescriptions can be inspected; the terminology can be tested by independent readers; the model-space diagnostic sequence can be preserved; future developments can be compared with the present baseline; criticism and alternative interpretations can be invited. The Zenodo record is not presented as a peer-reviewed publication. Its purpose is preservation, transparent disclosure of the work’s scope, and public access to an evolving line of investigation. Interpretation of the results The numerical results demonstrate only that prescribed combinations of thermal sensitivity, radial weighting, pairing suppression, composition thresholding, and projection can generate structured activity landscapes. They do not demonstrate that: irreversible accessibility is a fundamental physical field; entropy production determines subjective time; neutron-star matter contains the exact plotted layers; the prescribed model represents a realistic stellar interior; a microscopic algebra can generate the observed structures; the operational-clock interpretation is physically established. The strongest conclusion supported by the work is narrower: A physically active and highly organized medium may nevertheless contain spatially differentiated regions in which modeled irreversible pathways are more open, more restricted, or redirected by different mechanisms. Whether this phenomenological distinction can be derived from a deeper microscopic theory remains an open question. The purpose of the toy calculations in this preprint is not to establish that these structures occur in realistic stars. It is to demonstrate the diagnostic grammar by which distinct mechanisms can be separated and their spatial signatures compared before microscopic or observational inputs are introduced. Final note The manuscript is being shared before any claimed microscopic realization because a phenomenological target layer can be useful independently of whether a deeper theory is eventually successful. If a future microscopic framework reproduces, modifies, or rejects these diagnostic structures, the present work will provide a documented baseline against which that outcome can be compared.