Structural Irreversibility and Alysis: A Diagnostic Complement to Entropy in Macrostate Physics

This publication introduces alysis as a diagnostic principle for macroscopic irreversibility that is complementary to, but fundamentally distinct from, entropy. While entropy provides a statistical diagnostic of irreversibility under fixed levels of coarse-graining, alysis addresses a different question: whether a given macrostate description remains structurally admissible after irreversible loss of internal relational distinctions.

In this sense, alysis operates on macroscopic descriptions rather than on physical systems, states, or dynamical trajectories themselves. It evaluates the admissibility of a description under irreversible structural change, not the evolution of the underlying system.

Historically, diagnostics of irreversibility have been tied to statistical or dynamical quantities, leaving no explicit criterion for assessing the admissibility of macrostate descriptions themselves under irreversible structural loss.

Alysis is defined as an epistemic diagnostic, not as a dynamical law, physical observable, or quantitative measure. It does not describe time evolution, prescribe mechanisms, or enter physical equations. Alysis is not something to be computed, but a criterion of descriptive admissibility. It assesses whether the relational structure required to reconstruct a macrostate description in principle is still available. When such reconstruction is no longer possible under admissible operations, the macrostate description is said to undergo alysis.

The concept is motivated by boundary-based formulations of macroscopic irreversibility in which irreversible transformation occurs through boundary-localised aggregation and resolution of incoming relational structure. In these formulations, macrostates may persist even as internal distinctions are irreversibly eliminated. Alysis abstracts from this behaviour a general diagnostic criterion that does not depend on any specific boundary mechanism, formalism, or constructive implementation.

Importantly, alysis is not an alternative formulation of entropy and does not compete with thermodynamic or statistical laws. It does not quantify disorder, complexity, or information loss in a probabilistic sense. Instead, it complements entropy by identifying a structural threshold at which macrostate descriptions cease to be admissible, even when physical persistence or statistical description remains possible. In this way, alysis separates statistical irrecoverability from structural impossibility of reconstruction.

The manuscript places alysis in the broader context of macrostate physics and boundary-based frameworks, while keeping its definition independent of particular models, simulations, or visualisations. Set-theoretic constructions, pseudocode formulations, and computational implementations discussed in related work serve as illustrative contexts only and are not required for the validity of the diagnostic principle introduced here. The term structural refers to relational distinguishability within macrostates, not to mechanical integrity, material failure, or fracture processes.

This work is intended as a conceptual and architectural contribution. It introduces a precise vocabulary and a diagnostic distinction for analysing irreversible loss of structural admissibility in macroscopic descriptions across physics and related domains where persistence alone is insufficient to characterise irreversibility.

Earlier work introduced constructive boundary-based formulations of macrostate irreversibility, including explicit pseudocode formulations and illustrative computational implementations. The present manuscript abstracts from those constructions a diagnostic principle that stands independently of their specific implementation and does not rely on any particular formalism, algorithm, or model.