Information Erasure Inside the Quantum of Action

By maximizing entropy through Landauer information erasure within de Gosson's quantum of action, we show that continuum states collapse into discrete conjugate observables. Reflecting the experimental difficulty in isolating pure states, numerical results show that as action increases, Schrödinger-eigenstates become vanishingly sparse configurations—not privileged solutions—among the expanding possibilities in phase space. At the entropic limit of action, this work provides a thermodynamic-geometric correspondence to standard quantum mechanics.