Thermodynamic Relativistic Gravity--Classical General Relativity

This paper develops the curvature-energy formulation of the Thermodynamic Relativistic Gravity--Classical General Relativity(TRG--CGR) Framework. The framework proposes a thermodynamic description of gravitational curvature through three energy contributions: internal gravitational energy, pressure energy, and entropy energy. Beginning with the dimensionless gravitational field strength $\phi$, the paper develops these contributions step by step from the proposed TRG--CGR curvature relations.The internal gravitational energy is represented by $E_E$, the pressure energy contribution by $E_P$, and the scaled entropy energy by $E_S$. Two relativistic curvature correction coefficients are introduced: the discrete strong-field coefficient $\lambda_s$ and the continuous cosmological-field coefficient $\lambda_c$. The coefficients $1$, $1/2$, and $3/2$ are motivated through the weak-field expansion of the temporal metric component and the three-dimensional classical equipartition theorem.The paper further introduces the Duawo Energy Equivalent Principle (DEEP), which proposes that the total curvature energy of the universe is zero. The three energy contributions are combined to obtain a generalized total curvature-energy equation. Differentiating this equation with respect to radius produces the proposed TRG--CGR gravitational acceleration equation. An energy-space matrix is also constructed to examine the proposed energy modes, followed by the derivation of radius-dependent matter and entropy energy fractions using the proposed particle-horizon relationship $R_U=\pi R_H$.TRG--CGR is presented as a proposed hybrid extension of gravitational theory that connects classical Newtonian gravity, general relativity, thermodynamic gravity, emergent gravity, and modified gravitational dynamics. It is not intended to replace general relativity or the standard FLRW cosmological framework. The mathematical construction presented here establishes the internal structure of the proposed curvature-energy model, while its complete covariant formulation, parameter determination, and observational predictions require further investigation.