Entropy Redistribution as the Mechanism of Apparent Nonlocal Wavefunction Collapse

We present a mathematically rigorous framework demonstrating that the apparent nonlocal "collapse" in bipartite entangled quantum systems emerges naturally from local entropy redistribution during measurement. By treating measurement as a unitary coupling between system A and an observer apparatus O described by the interaction Hamiltonian HAO = ℏπ 2t 0 1 i=0 |i⟩⟨i| A ⊗ (|0⟩⟨i| O + |i⟩⟨0| O), we track the evolution of von Neumann entropy S(ρ) = −Tr(ρ ln ρ) across all subsystems. For a maximally entangled Bell state Φ + = 1 √ 2 (|00⟩ + |11⟩), we derive closed-form expressions showing that while subsystem B's reduced density matrix ρB remains locally unchanged, the apparatus entropy increases from zero to ln 2, with the global entropy S(ρABO) increasing by exactly the Shannon entropy of measurement outcomes. We prove a general entropy balance theorem establishing that for any projective measurement on entangled systems, ∆S global = H({pi}), where H({pi}) is the Shannon entropy of outcome probabilities. Our numerical simulations in finite-dimensional Hilbert spaces demonstrate the precise temporal dynamics of entropy flows during measurement, confirming the thermodynamic consistency of our approach. This framework resolves the apparent tension between quantum nonlocality and relativistic causality, eliminates the need for a separate collapse postulate, and provides a unified mechanism connecting quantum measurement, decoherence, and thermodynamic irreversibility-all within standard unitary quantum mechanics.