Thermodynamic Relativistic Gravity--Classical General Relativity

This paper presents the thermodynamic state-space foundation of the Thermodynamic Relativistic Gravity--Classical General Relativity (TRG-CGR) Framework. The framework is formulated as a proposed extended-gravity approach that connects thermodynamic state variables, horizon thermodynamics, gravitational energy, spacetime curvature, and cosmological geometry. Starting from the thermodynamic state function \(E=E(S,V)\), the first law of thermodynamics and its corresponding Maxwell relation are developed. A proposed relation, referred to as the Duawo Planck Horizon Law, is then introduced to connect the Planck length and Planck temperature with the temperature and circumference of the Hubble horizon. This relation is used to obtain a horizon-temperature expression and a temperature-ratio representation of horizon entropy.The paper subsequently develops a Schwarzschild-radius relation using an escape-energy argument and applies the resulting horizon mass to the relativistic energy expression. By differentiating the energy and entropy with respect to the spherical horizon volume, the framework obtains proposed expressions for the energy-density gradient, pressure, curvature scale, and emergent cosmological constant. The resulting thermodynamic relation is then mapped onto the metric tensor through four proposed quantities: the Energy-pressure-momentum tensor, the Pressure/Curvature tensor, the Emergent Cosmological Constant, and the Duawo Entropy Tensor.The paper concludes by presenting the proposed TRG-CGR field equations. The results establish the mathematical structure proposed in this paper. Their physical interpretation, tensorial consistency, compatibility with established gravitational field equations, and observational implications require further analytical and experimental investigation.