Quantized Phase-Space from Information Erasure

The Second Law of Thermodynamics applied to the symplectic quantum of action maximizes en- tropy by erasing surplus information within the minimal Heisenberg cell, manifesting a complexity- action duality. The resulting collapse transforms the continuum into a quantized geometry. Numer- ical analysis of the harmonic oscillator demonstrates that this geometry recovers the marginals of the Wigner distribution. These results suggest quantized phase space is a thermodynamic necessity, providing quantum mechanics with a geometric correspondence independent of probability waves.