Wave Function Collapse as Minimum Information Cost

This paper proposes the Minimum Information Cost Principle (MICP): wave function collapse is governed by the local thermodynamic cost of recording each possible outcome in the environment. The realized outcome minimizes the total Landauer erasure energy. The principle synthesizes four prior results from Complexity Binding Theory—Born's rule as thermodynamic equilibrium, uniqueness of the Shannon cost function, the 1-bit theorem for weak decays, and the coherence trade-off in parity violation—into a unified framework. The paper derives four testable predictions: (1) measurement cost scales as kT·H(p); (2) a parameter-free decoherence rate γ = γ₀ ln2 / H(p) that depends on the Shannon entropy of the branch probabilities, testable in the Landauer-limited regime; (3) electroweak parity restoration as a thermodynamic phase transition (already confirmed); and (4) mass-independent decoherence at the Landauer floor, directly distinguishing MICP from Penrose's gravitational collapse—testable using momentum-entangled helium isotopes (³He*/⁴He*) on existing experimental platforms. Prediction (2) is falsifiable with no free parameters. A null result would kill the theory.