Entropic Causal Holography: Information-Theoretic Past Hypothesis via a Boundary Monotone

The arrow of time is thought to originate from a low-entropy Past Hypothesis, while the holographic
principle suggests our universe is encoded on a boundary. We propose Entropic Causal Holography (ECH), a comprehensive testable framework that unifies these fundamental concepts. We recast the Past Hypothesis as a holographic boundary state with low information complexity rather than low entropy, introducing a computable boundary monotone M_ε(t) based on regularized quantum relative entropy to quantify the growth of this complexity under chaotic evolution. Our central conjecture posits that the monotonic growth of M_ε(t) is universally dual to the growth of bulk spacetime volume. This work provides a complete theoretical foundation for ECH, supported by extensive analytical and numerical evidence from AdS-Vaidya spacetimes, the Sachdev-Ye-Kitaev (SYK) model, and Jackiw-Teitelboim (JT) gravity, establishing a new, empirically testable link between quantum information theory and the emergence of time itself.