A theoretical preprint on arXiv examines what happens to fermionic quantum systems when they experience decoherence, the process where interaction with the environment turns pure quantum states into mixed ones. Starting from an initial Gaussian free-fermion state, the authors derive an inequality proving that a class of Rényi-2 correlators in the resulting decohered state are strictly upper-bounded by the correlator that signals strong-weak spontaneous symmetry breaking (SW-SSB) of the charge-U(1) symmetry. This bound holds for any decoherence strength and implies that environmental noise tends to drive these systems toward U(1) SW-SSB. The work is purely analytical with no experiments or sample sizes, connects the result to projected quantum spin Hall insulators and Dirac spin liquids, and remains a preprint that has not been peer-reviewed. Limitations include its restriction to specific correlators and initial Gaussian states, meaning broader applicability requires further validation.