Galaxy Rotation Curves and Dark Energy from the Perspective of Gravitational Entropy: The GEE Framework

We propose an axiomatic framework, the GEE framework, based on gravitational dissipative structures and the holographic principle. In this framework, the observational effects known in the standard cosmological model as "dark matter" and "dark energy" are reinterpreted as effective projections of gravitational degrees of freedom during the coarse-graining process. The core mathematical contributions are six theorems: the boundary value problem for the fusion of gravitational relaxation and holography (Theorem 4.1), the defining relation for the temperature ratio (Theorem 4.2), the dissipative virial theorem (Theorem 4.3), the exact solution of the k-essence Lagrangian (Theorem 6.1), the derivation of the GO cutoff from the apparent horizon (Theorem 6.2), and the analytical expression for the mass function integral (Theorem 7.1). Two temperatures exist: the thermodynamic temperature and the gravitational entropy temperature . The temperature ratio evolves with the universe, driving the Hubble parameter from to , with . The dissipative virial theorem predicts that the standard virial theorem overestimates mass by about 1.5–2.4 times; three observational data sets support this prediction at the order-of-magnitude level. GEE V2.0 adopts a nine-parameter system. Its statistical status is indistinguishable from the standard cosmological model under current combined data, while under Planck data alone the standard model is preferred. The framework provides a unified language and falsifiable criteria for rotation curves, accelerated expansion, and the Hubble tension.