Entropic Interpretation of Wave Function Collapse

We propose an information-geometric, entropic interpretation of wave function collapse based on the finite distinguishability between quantum states. By analyzing the second-order expansion of relative entropy, we show that collapse can be understood as a finite transition in state space governed by the Fisher information metric. This framework naturally assigns an energetic cost to collapse, identified with the canonical energy associated with the perturbation. The resulting picture provides a unified description linking quantum measurement, statistical distinguishability, and geometric structure.