Current Symmetries for Particle Systems with Several Conservation Laws

We consider stochastic interacting particle systems with more than one conservation law in a regime far from equilibrium. Using time reversal we derive symmetry relations for the stationary currents of the conserved quantities that are reminiscent of Onsager's reciprocity relations. These relations are valid for a very large class of particles with only some mild assumption on the decay of stationary relations and imply that the coarse-grained macroscopic dynamics is governed by a system of hyperbolic conservation laws. An explicit expression for the conserved Lax entropy is obtained.