CUP-Ω∗: a covariant GKLS–Einstein–Langevin universal equation for thermodynamically consistent quantum–informational dynamics in the CUCE/Spinoza/Hilbert framework

We formulate CUP-Ω∗ as a covariant evolution law for a quantum state functional defined on Cauchy hypersurfaces. The generator combines Tomonaga–Schwinger hypersurface dynamics with a covariant GKLS dissipator constructed from modular jump operators relative to a unified thermodynamic target state. Under explicit locality and integrability conditions, the evolution is foliation independent. Under detailed balance and primitivity assumptions, the quantum relative entropy to the target state provides a Lyapunov functional, ensuring a second-lawtype monotonicity and exponential convergence to a unique attractor. We further couple the matter dynamics to an Einstein–Langevin stochastic semiclassical gravity equation to encode stress-tensor fluctuations and back-reaction consistently. Finally, we derive falsifiable, quantitative constraints—finite-step Choi positivity, order-independence under spacelike update exchange, and monotone relative entropy decay—that can be tested in controlled open quantum platforms and interpreted as physically grounded stability principles for learning-like dynamics.