Statistical control of relaxation and synchronization in open anyonic systems

Quantum statistics dictate how particles exchange and correlate-but in two-dimensional systems, these rules extend beyond bosons and fermions to anyons, quasiparticles with continuously tunable exchange phases. Here, we develop a Lindblad framework for anyonic oscillators and show that fractional statistics enable statistical control of decoherence in open quantum systems. By varying the anyonic phase and environmental correlations, we demonstrate tunable mode protection, identify exceptional points in the dissipative spectrum, and reveal temperature-dependent coherence bifurcations. We also demonstrate that signatures of the statistical phase should also be manifest in 2D coherent spectroscopic probes of these systems. These results establish the exchange phase as a functional control parameter for engineering dissipation-resilient quantum states.