Abstract

We show that non-equilibrium features of an anyonic system can be effectively captured through "effective equilibrium", a concept that can be characterized by two parameters: effective chemical potential and effective temperature. This concept further facilitates the analysis of effective linear response in charge and heat currents around the anyonic "Laughlin surface" (a generalization of the Fermi surface to the case of out-of-equilibrium anyons). We show that in the absence of real anyon tunneling or collisions, the dynamics are primarily governed by anyonic time-domain braiding processes, resulting in symmetry between particle and hole distributions, as well as the vanishing of Seebeck and Peltier coefficients. We further show that anyonic time-domain braiding induces the notion of "hot anyons", an anyonic-unique feature that can be experimentally detected via our proposed witness function. When real-particle tunneling and collisions are included, this symmetry is however broken, producing finite Seebeck and Peltier coefficients. These coefficients thus serve as robust indicators of the influence of real-particle tunneling and collisions, thereby advancing our understanding of non-equilibrium dynamics in anyonic systems.