A Thermodynamic Framework for Unified Equation of State: Deriving Atomic Structures and Emergent Quantum Behaviors in Chemical Systems

In this work, we present a novel unified equation of state (UEOS) that integrates thermodynamic variables across all phases of matter, challenging longstanding paradigms in quantum mechanics and statistical physics. By deriving the UEOS from first principles combining relativistic invariance and nonlocal field interactions, we demonstrate that particle-wave duality emerges as an artifact of incomplete classical approximations rather than a fundamental property of quantum systems. Our analysis reveals those apparent dual behaviors in phenomena such as the double-slit experiment stem from emergent statistical fluctuations in the UEOS, effectively debunking the need for intrinsic duality and reconciling quantum observations with a purely field-theoretic framework. Furthermore, entropy is reinterpreted not as a measure of disorder but as a pseudo-thermodynamic quantity arising from incomplete knowledge of the UEOS parameters, resolving paradoxes in information theory and black hole thermodynamics. Finally, the UEOS elucidates the mystery of phase transitions by providing a continuous analytic function that predicts critical points without invoking symmetry breaking or renormalization group flows, offering exact solutions for van der Waals-like behaviors in real gases and superconductors. This unified approach not only simplifies the theoretical landscape but also suggests experimental tests via high-precision calorimetry and interferometry, paving the way for a paradigm shift in foundational physics.