Thermodynamic Relativistic Gravity - Classical General Relativity (TRG-CGR) Framework: Thermodynamic State Space

This paper presents the thermodynamic state-space foundation of theThermodynamic Relativistic Gravity--Classical General Relativity(TRG-CGR) Framework. The framework is formulated as a proposedextended-gravity approach that connects thermodynamic state variables,horizon thermodynamics, gravitational energy, spacetime curvature,and cosmological geometry. Starting from the thermodynamic statefunction \(E=E(S,V)\), the first law of thermodynamics and itscorresponding Maxwell relation are developed. A proposed relation,referred to as the Duawo Planck Horizon Law, is then introduced toconnect the Planck length and Planck temperature with the temperatureand circumference of the Hubble horizon. This relation is used toobtain a horizon-temperature expression and a temperature-ratiorepresentation of horizon entropy. The paper subsequently develops a Schwarzschild-radius relationusing an escape-energy argument and applies the resulting horizonmass to the relativistic energy expression. By differentiating theenergy and entropy with respect to the spherical horizon volume, theframework obtains proposed expressions for the energy-densitygradient, pressure, curvature scale, and emergent cosmologicalconstant. The resulting thermodynamic relation is then mapped ontothe metric tensor through four proposed quantities: theEnergy-pressure-momentum tensor, the Pressure/Curvature tensor, theEmergent Cosmological Constant, and the Duawo Entropy Tensor.The paper concludes by presenting the proposed TRG-CGR fieldequations. The results establish the mathematical structure proposed in thispaper. Their physical interpretation, tensorial consistency,compatibility with established gravitational field equations, andobservational implications require further analytical andexperimental investigation.