Entropic Hysteresis of Spacetime: A Quantum Gravity Framework for Dark Matter and Dark Energy

In this work we present a unified model for phenomena that remain unexplained, inter-preted as dark matter and dark energy—based on the hypothesis that gravity emerges fromlocal entropy variations. Our approach integrates non-Markovian dissipative dynamics, amechanism of entropic hysteresis of spacetime, and the holographic principle, suggest-ing that the spacetime fabric retains a "memory" of its past configurations. This memory,modulated by the dimensionless parameter η, establishes the coupling between the in-formational flux—expressed via the derivative ∂S(ϕ)/∂ϕ—and the geometric curvature.The model, which rigorously connects with Einstein’s relativity by introducing a correc-tive term ∆μν (ϕ) (see Appendix A for analytical details), draws inspiration from LoopQuantum Gravity and Spin Foam models, from which discrete scales (e.g. the area gapdetermined by the Immirzi parameter) emerge to provide a microscopic anchoring for η.Furthermore, the work compares the theoretical predictions with observational data, suchas the misalignment observed in the Bullet Cluster and galactic rotation curves, throughnumerical simulations and sensitivity analyses (see Appendix B). The document includesgraphs, diagrams, and a glossary of technical terms. Keywords: Entropic Gravity, SEAT, Dark Matter, Dark Energy, Loop Quantum Gravity, Spin-Foam, Hysteresis, HPC PDE Simulations, Vacuum Fine-Tuning, Hubble Tension, Cosmology, Observational Data, SPARC, EPRL-FK