Noise-induced decoherence-free zones for anyons

We develop a stochastic framework for anyonic systems in which the exchange phase is promoted from a fixed parameter to a fluctuating quantity. Starting from the Stratonovich stochastic Liouville equation, we perform the Stratonovich–Itô conversion to obtain a Lindblad master equation that ties the dissipator directly to the distorted anyon algebra. This construction produces a statistics–dependent dephasing channel, with rates determined by the eigenstructure of the real symmetric correlation matrix $D_{ab}$. The eigenvectors of $D$ select which collective exchange currents – equivalently, which irreducible representations of the system – are protected from stochastic dephasing, providing a natural mechanism for decoherence-free subspaces and noise-induced exceptional points. The key result of our analysis is the universality of the optimal statistical angle: in the minimal two-site model with balanced gain and loss, the protected mode always minimizes its dephasing at ${\theta }^{\star }=\pi \mathrm{/}2$, independent of the specific form of $D$. This robustness highlights a simple design rule for optimizing coherence in noisy anyonic systems, with direct implications for ultracold atomic realizations and other emerging platforms for fractional statistics.