Emergent Arrow of Time Induced by Boundary Observations in the SYK-Lindbladian Model

A central question in the quantum-gravitational description of our universe is how the arrow of time emerges from a fundamentally timeless theory. Reference 1 proposed that an intrinsic, self-referential mechanism—encoded in a nonlocal operator acting on a holographic tensor network—breaks the global Wheeler-DeWitt constraint and drives the monotonic growth of entanglement entropy, thereby giving rise to an internal time. The present work provides the first exactly solvable and numerically testable microscopic realization of this mechanism within the open Sachdev-Ye-Kitaev (SYK) model. By interpreting Lindblad jump operators as directed information extractions from network degrees of freedom, we prove, via large- Schwinger-Keldysh field theory and finite- exact diagonalization (up to ), that the entanglement entropy of the observed subsystem increases monotonically and irreversibly, that the level-spacing distribution transitions from Poisson to Wigner-Dyson universality, and that the dissipative form factor displays a sharp, first-order dynamical phase transition. A control experiment employing structureless, nonlocal Lindblad jumps fails to produce these signatures simultaneously, confirming that they are specific consequences of the self-referential mapping rather than generic features of open quantum systems. We further propose a holographic dictionary in which the dissipative coupling is dual to the boundary cosmological constant in Jackiw-Teitelboim gravity, offering a concrete, testable bridge between the self-referential operation and the geometry of emergent spacetime. These findings establish a compact, computable, and—crucially—experimentally accessible microscopic foundation for the hypothesis that time is born from quantum information processing, and they provide a theoretical blueprint for observing the emergence of an arrow of time on near-term quantum simulators.