Fluctuation Relations for Currents

We consider a non-equilibrium statistical system on a graph or a network. Identical particles are injected, interact with each other, traverse, and leave the graph in a stochastic manner described in terms of Poisson rates, possibly strongly dependent on time and instantaneous occupation numbers at the nodes of the graph. We show that the system demonstrates a profound statistical symmetry, leading to new Fluctuation Relations that originate from the supersymmetry and the principle of the geometric universality of currents rather than from the relations between probabilities of forward and reverse trajectories.