Connectivity Engineering: Irreversible Entropy Accumulation Induced by Topological Quenching and the Arrow of Time

The contradiction between the thermodynamic arrow of time and microscopic dynamical reversibility is a core problem in statistical physics. Within the framework of connectivity engineering, this paper proposes a new mechanism: irreversible accumulation of subsystem entropy caused by topological quenching. We numerically simulate the cyclic switching of a one-dimensional spin network between topological steps k=1 and k=4. Results show that each switch from the highly connected state to the frustrated state leads to an irreversible "fall" of information into the local entanglement space; when switched back to the initial topology, the subsystem entanglement entropy cannot recover to its initial value, but instead surges from 0 to approximately 2.96 and remains in the saturation regime, exhibiting a unidirectional entropy accumulation. Since the theoretical maximum entropy of this subsystem is 3.0, this irreversible saturation directly reveals the limit of information coarse-graining. The above results prove that the microscopic origin of the arrow of time is precisely the information scrambling caused by the irreversibility of underlying geometric topological reconstruction.