Optical Metric from Local Information Volume Conservation and the Entropic Derivation of Einstein Equations

From the perspective of Quantum Cellular Automata (QCA) and information ontology, spacetime geometry should be understood as an emergent representation of the information processing capacity and connectivity structure of an underlying discrete quantum network. In this framework, we propose and formalize the principle of "Local Information Volume Conservation": in the coarse-graining process from discrete QCA to a continuous effective manifold, the "total amount of distinguishable quantum degrees