Numerical Simulation of an Emergent Arrow of Time via Self-Referential Quantum Circuits

We present a numerical simulation demonstrating that a self-referential quantum operation induces a directed, statistically robust monotonic growth of entanglement entropy in an observed subsystem. Drawing on the theoretical proposal that the arrow of time originates from directed information extraction within a quantum system , we design a minimal 4-qubit circuit initialized in the pure product state , so that subsystem starts with zero entanglement entropy. A self-referential layer, realized by controlled-NOT gates from subsystem to environment followed by randomization of , periodically extracts information from . Using IBM Qiskit's local simulator, we measure the entanglement entropy as a function of circuit depth. Under self-referential dynamics, exhibits a strongly significant monotonic trend (Spearman ), while two control circuits—one with symmetric - coupling () and one with reversed directional coupling ()—show significantly weaker or absent monotonicity. We discuss the limitations of interpreting this simulation as a full realization of thermodynamic irreversibility, and clarify that the observed monotonic entropy increase is a necessary but not sufficient condition for a genuine arrow of time. This work provides a minimal, accessible testbed for exploring the information-theoretic origins of temporal irreversibility .