Emergent Lorentzian Geometry from Quantum Criticality: Dynamic Signature Change via Relative Entropy Instability

This paper introduces a novel framework for analog gravity in which an effective (2+1)-dimensional Lorentzian spacetime emerges dynamically on the information geometry of a driven open quantum system. Unlike traditional fluid-based analogs, the spatial fabric is provided by the Quantum Fisher Information Metric (QFIM) over a control-parameter manifold, while laboratory time serves as the temporal axis. Using Keldysh nonequilibrium field theory, the study demonstrates that the Lorentzian signature and thus the existence of causal light cones-originates fundamentally from the thermodynamic passivity of the quantum state. This profound connection makes the causal structure a tunable, falsifiable property: driving the system into population inversion triggers a signature-breakdown transition that destroys the hyperbolicity of the emergent spacetime. Supported by exact derivations for a two-qubit model and concrete experimental protocols involving continuous homodyne detection and FPGA-based feedback, the research offers a fully measurable laboratory platform to explore the intersection of quantum information geometry, nonequilibrium thermodynamics, and emergent causal structure. By Gökay Yıldız gokay@krekpot.com