Foundational Physical Framework for Exploring Potential Solutions for a Comprehensive Equation of State EOS

This study addresses the longstanding challenge in thermodynamics: the persistent inability to develop a comprehensive Equation of State (EOS) that overcomes the limitations of semi-empirical models, which remain focus in restricted conditions and materials. This recurring pattern highlights the necessity for a principled framework capable of enhancing predictive power and understanding of the physical relationships underlying thermodynamic behavior. Accordingly, present work introduces a foundational physical framework designed to serve as a rigorous analytical tool and a robust methodological roadmap, supporting future research dedicated to constructing predictive EOS formulations. The framework is built upon the Uniformity Rule of Physical Significance and Numerical Magnitude of Fundamental Quantities, which redefines the physical meaning and numerical values of the primary quantities, mass, space, and time, within balanced physical relations. The framework further generalizes the natural units into extreme properties intrinsically associated with every object according to its mass, classified into dual quantum and gravitational domains, both intrinsically linked to the universal constants. Through detailed numerical analysis, the framework structure demonstrated highly internal consistency. This analysis led to the theoretical proposition of two derived quantum constants (ℳ and Kq), introduced to address a symmetry gap between the gravitational and quantum realms, and precise symmetrical correlations among the fundamental constants. These structural relations constitute the essential methodological foundation needed to guide future efforts toward the development of fully operational and comprehensive equation of state models. The structural capabilities of the framework also reveal its potential to unify perspectives across diverse fields of physics, from thermodynamics and electromagnetism to mechanics and cosmology, thereby reinforcing its promise as a reliable foundation for future scientific advancement.