An Axiomatic Informational Framework for Entropy, Emergence, and Organization

Abstract Entropy is a central concept across physics, biology, and information theory, yet its conceptual foundations remain fragmented across domain-specific formalisms. In statistical mechanics, entropy quantifies microstate multiplicity; in information theory, it measures uncertainty relative to an observer; in thermodynamics, it governs irreversible macroscopic behavior; and in complex systems, increasing organization appears to coexist with entropy production. These perspectives are empirically successful, but conceptually misaligned.This work presents an axiomatic informational framework that clarifies the structural assumptions underlying entropy, emergence, and organization. Rather than introducing new dynamical laws or replacing existing formalisms, the framework makes explicit the informational conditions under which such descriptions arise. Information is defined as distinguishability under constraint, while entropy emerges as a derived measure of inaccessible distinctions under scale- and boundary-dependent coarse-graining. Within this view, informational structure is conserved, while informational accessibility is redistributed through interaction. Apparent irreversibility and emergent organization arise naturally from asymmetries of access across descriptive levels. The framework offers a unifying interpretive foundation for entropy without competing with established physical theories.