Decoherence as a Phase Transition: An Information-Theoretic Account of the Quantum-to-Classical Boundary.

This paper presents a formal framework framing quantum decoherence as an information-theoretic phase transition at the quantum-to-classical boundary. We demonstrate that environment-induced superselection (einselection) can be characterized as a true dynamical phase transition where the system-environment coupling strength acts as a thermodynamic control parameter, and the suppression of off-diagonal density matrix elements functions as an order parameter analogous to magnetization in the Ising model. Using quantum mutual information, von Neumann entropy, and entanglement entropy, we track the operational flow of information from a quantum system into environmental degrees of freedom, demonstrating how a singular classical reality emerges via the redundant copying of pointer states into environmental fragments—a process governed by Quantum Darwinism. We analyze a simulated spin-boson model and random unitary circuits with tunable dissipation, extracting clear signatures of criticality including power-law scaling and diverging correlation times at a critical threshold . Crucially, we connect this behavior to recent advancements (2023–2025) in mixed-state topological order, establishing that decoherence-induced transitions map onto anyon condensation transitions within an errorfield double formulation. Finally, we explore the foundational implications of this framework: it sharpens the measurement problem via informational symmetry breaking, reframes observation as a high-decoherence thermodynamic limit, and introduces a Gödelian perspective by demonstrating that determining the critical threshold for arbitrary many-body environments is formally undecidable due to the non-computability of the spectral gap in the thermodynamic limit.