Quantum state complexity and the thermodynamic arrow of time

Why time is a one-way corridor? What's the origin of the arrow of time? We attribute the thermodynamic arrow of time as the direction of increasing quantum state complexity. Inspired by the work of Nielsen, Susskind and Micadei, we checked this hypothesis on both a simple two qubit and a three qubit quantum system. The result shows that in the two qubit system, the thermodynamic arrow of time always points in the direction of increasing quantum state complexity. For the three qubit system, the heat flow pattern among subsystems is closely correlated with the quantum state complexity of the subsystems. We propose that besides its impact on macroscopic spatial geometry, quantum state complexity might also generate the thermodynamic arrow of time.