Beyond Semiclassical Approximations: Entanglement Flow, Nuclear Decay Channels, and Environmental Structure in Radical Pair Magnetoreception

Radical pair magnetoreception is often modeled using semiclassical approximations in which nuclear spins are replaced by effective magnetic fields. Here, we develop and analyze a fully quantum mechanical radical pair model to determine when such approximations fail and to identify mesoscopic regimes in which genuinely quantum effects become dynamically relevant.

The model consists of two interacting electron spins coupled to explicit nuclear spin environments through anisotropic hyperfine interactions, with exchange and dipolar couplings retained as independently tunable parameters. Open-system effects are introduced using a Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) master equation as a controlled Markovian baseline.

We first quantify thermalization behavior via trace-distance convergence of reduced subsystems. We then directly compare the full quantum nuclear model with the semiclassical Overhauser-field approximation under both unitary and open-system evolution, identifying parameter regimes where semiclassical treatments fail to capture coherent oscillations and correlation structure.

A central result is the explicit tracking of entanglement and entropy flow between the radical pair and its nuclear environment. Subsystem von Neumann entropies and bipartite entanglement measures reveal oscillatory exchange of quantum correlations between electrons and nuclei, demonstrating information backflow and non-Markovian regimes characterized by coherence revivals rather than monotonic decay. These dynamics cannot be reproduced by purely classical noise models.

Beyond static environments, we introduce a hypothetical nuclear decay mechanism modeled as a local quantum channel acting on nuclear subsystems. This quantum-information description embeds decay directly into the radical pair Hilbert space, allowing its effects on entanglement redistribution and information flow to be quantified.

Together, these results recast radical pair magnetoreception within a quantum information framework, highlighting regimes where environmental structure, entanglement flow, and engineered nuclear processes qualitatively reshape spin dynamics.