Entropic Ratio of Identity (EROI): A Structural Framework for Constraint and Viability

This work introduces the Entropic Ratio of Identity (EROI) as a structural framework for analyzing the relationship between constraint, freedom, and viability in complex systems.

EROI is defined as the ratio between structural load and structural freedom.

Within this formulation, structural load represents the set of constraints or pressures acting on a system, while structural freedom represents the degrees of interaction available to maintain functional identity.

The framework proposes that system identity and viability can be classified according to structural regimes determined by the value of EROI. These regimes include regions of structural margin, structural balance, increasing restriction, and transition or collapse. The framework also introduces two related concepts:

• HROI (Holistic Ratio of Identity), describing identity preservation in mathematical or structural systems.
• SDI (Structural Decomposition of Identity), describing how complex identities can emerge from combinations of lower-level subsystems.

The document develops a formal description of these concepts and explores their interpretation across multiple domains, including:

• atomic and nuclear systems

• biochemical processes such as fermentation

• computational and neural network systems

• astrophysical systems including stellar stability

• quantum-scale interactions

The framework does not attempt to replace existing physical theories. Instead, it proposes a structural classification tool that may help describe the viability and stability of systems under internal and external constraints.

Special attention is given to the distinction between instantaneous structural balance and temporal viability, introducing a cumulative imbalance formulation to describe transitions over time.

This repository contains the Version 1 (V1) of the framework, representing a formal and extended development of the EROI/HROI model.

Future work will explore mathematical formalization, additional theoretical implications, and potential applications across physics, complex systems, and computational models.