We derive a set of thermodynamic-geometric relations directly from the principle of instantaneous mass-energy conservation in General Relativity, revealing a deep interplay among thermodynamics, dynamics, and spacetime curvature. The derivation rests solely on the framework of General Relativity augmented by a single thermodynamic ansatz concerning entropy generation during acceleration. A central advance of this work is the formulation of a kinetic energy that remains well-defined in generic curved spacetimes lacking global timelike Killing vectors. This formulation naturally yields a universal analytic framework for predicting mass defects—including gravitational binding energy, nuclear binding energy, and annihilation energy—as limiting cases of a single relational expression. The framework is quantitatively tested against publicly available observational data from the GW150914 binary black hole merger, showing excellent agreement with the reported final mass without introducing free parameters. By treating kinetic energy as an inherently instantaneous quantity in the absence of global time-translation symmetry, the resulting relations illuminate the irreducible connection between gravity, inertia, and thermodynamic irreversibility. This approach may provide a concrete steppingstone toward a thermodynamic reformulation of General Relativity.
Chaojie Shi (Sat,) studied this question.