Entropy-Paid History Selection as a Physical Contribution to the Muon Anomalous Magnetic Moment

The muon anomalous magnetic moment remains one of the most persistent discrepancies between experiment and Standard Model prediction. Existing explanations invoke either hadronic uncertainties or new particle degrees of freedom. Here we propose a third explanatory class: a thermodynamic residual arising from entropy-paid stabilization of a recordable muon spin history in an open quantum environment. We parameterize the excess as where is the irreversible entropy cost required to select and stabilize a persistent measurement branch. Matching the Fermilab excess implies , corresponding to bits of erased superposition under Landauer bookkeeping. This value is consistent, at the order-of-magnitude level, with vacuum mode counting at the electroweak scale. Crucially, this framework predicts a sign-definite dependence of on environmental entropy flux and sharp cross-lepton constraints, providing falsifiable tests that distinguish it from mediator-based explanations. If validated, this result identifies entropy-paid history selection as a previously unrecognized thermodynamic contribution to the foundations of precision quantum measurement. Keywords: Muon anomalous magnetic moment, quantum thermodynamics, open quantum systems, entropy production, precision measurements, quantum measurement theory, Landauer principle, nonequilibrium statistical mechanics, environmental decoherence, large deviation theory.