Flux freezing — the idea that magnetic field lines move with the plasma — is a cornerstone of magnetohydrodynamics. But in turbulent plasmas, it fails. Field lines disconnect, reconnect, and diffuse in ways that the frozen-in approximation can't describe.
The authors (arXiv:2603.22526) replace field lines with magnetic pathlines: curves that follow the plasma's velocity field through time. Unlike field lines (which are instantaneous spatial curves), pathlines track the actual trajectory of material elements and the flux they carry.
In the new framework, statistical flux freezing holds: while individual pathlines diverge chaotically, the statistical distribution of magnetic flux along pathlines is conserved. The turbulent fluctuations that break deterministic flux freezing preserve the statistical version.
The through-claim: flux freezing fails pointwise in turbulence but holds statistically. The fix isn't better approximations to the frozen-in condition — it's changing the mathematical object from field lines to pathlines. Field lines are geometric; pathlines are dynamical. The dynamical objects preserve the conservation law that the geometric objects lose.