Decoherence-Driven Curvature: A Thermodynamic Origin for Spacetime Geometry

We propose that spacetime curvature emerges not only from classical stress-energy, but also fromthe irreversible quantum decoherence of geometry. Building on earlier models that treat time and ge-ometry as quantum-coherent degrees of freedom entangled with matter fields, we construct a frame-work in which decoherence suppresses interference between geometrical configurations, inducing anentropy functional Sdecoh[g]. Variation of this entropy defines a tensor Dμν that sources curva-ture, leading to a generalized gravitational field equation recovering Einstein gravity in the classicallimit. Our construction is semiclassical, observer-dependent, and applies in regimes where reduceddensity matrices diagonalize into pointer-state geometries. We test the proposal in Schwarzschildand FLRW spacetimes using entropy-based ansätze, and outline possible experimental signaturesin matter-wave interferometry. While preliminary, these results support a view of gravity as themacroscopic imprint of quantum information loss.