Symmetry Classification of Quantum Thermalization under Bounded Decoherence Constraints: Analytical Model, Numerical Simulation, and Experimental Predictions

We investigate the fate of symmetries during quantum thermalization under the hypothesis that decoherence rates are subject to a global bound (bounded decoherence conjecture). We prove a Thermalization Symmetry Classification Theorem showing that symmetries of the pre-thermal state partition into three classes under bounded Fokker–Planck dynamics: (I) broken symmetries, selected by drift toward pointer states; (II) preserved symmetries, maintained by divergence-free circulation currents; and (III) bounded symmetries, whose breaking rates saturate at the decoherence bound β_max. We substantiate the classification with two independent calculations. First, an analytically solvable model: a dissipative rotor on S¹ with Mexican-hat potential, for which we compute the Kramers escape rate, the symmetry-breaking timescale, and the steady-state circulation current in closed form, demonstrating all three symmetry phases as functions of the bound. Second, a numerical Langevin simulation of 10⁴ trajectories on a two-dimensional order-parameter manifold, which confirms the analytical predictions and visualizes the three phases through probability density evolution and current maps. Both calculations yield a new, falsifiable prediction: a minimum symmetry-breaking timescale τ_min = 2π/(ω₀ · β_max) that has no analogue in standard Lindblad theory. Combined with the previously derived GHZ saturation and channel trade-off predictions, this provides four independent experimental signatures. The entire analysis uses only standard physics (Holevo channel capacity, Landauer principle, Fokker–Planck dynamics, Kramers theory) and makes no assumptions beyond the bounded decoherence conjecture.