The Pressure State Scalar: A Rigorous Derivation of Coherence in Thermodynamic Systems

📘 Abstract: This paper introduces the Pressure State Scalar (PSS), a scalar field metric that formalizes the emergence of coherence within thermodynamic systems. Rooted in a field-primary ontology, the PSS framework demonstrates how nested toroidal dynamics, pressure gradients, and rotational symmetries give rise to self-organizing structures across quantum, biological, and cosmological scales. The derivation bridges classical thermodynamic concepts with modern field theories, offering a unified approach that reframes entropy not as disorder, but as a gradient toward structured coherence. The paper further illustrates the practical implications of the PSS for engineering, materials science, and systems biology .