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We develop a unified information-theoretic framework in which causal structure, locality, geometry, and gravitational dynamics emerge directly from the dynamics of open quantum systems. Starting from a Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) master equation with quasi-local interactions, we demonstrate that the modular generator K = −log ρ inherits a finite-speed propagation bound, establishing an intrinsic causal structure without assuming spacetime a priori. We construct an information-geometric description of quantum states using a monotone Riemannian metric derived from the second variation of entropy. Within this framework, we show that the curvature tensor is controlled by the nonlinear structure of entropy and that critical behavior corresponds to geometric singularities. A key result is the identification of the effective source tensor as the covariant Hessian of entropy production, defined via the relative entropy dissipation rate under GKSL dynamics. This leads to a closed, covariant set of equations of the form Gab = κ∇a∇bΦ(ρ), where Φ(ρ) is the entropy production functional. We further demonstrate that spatial distance can be defined operationally through mutual information, yielding an emergent spacetime metric consistent with the causal bound. Our results establish a direct pathway from microscopic open quantum dynamics to emergent spacetime structure and provide a mathematically consistent realization of gravitational dynamics as an information-geometric response to entropy flow. This framework offers a concrete mechanism for the emergence of locality and geometry, bridging quantum information theory, non-equilibrium dynamics, and gravitational physics.
Nesen O. I. 2026. Universal Modular Dynamics and the Emergence of Causal Locality from GKSL Open-System Dynamics. PREPRINTS.RU. https://doi.org/10.24108/preprints-3115100
