  We examine a class of one-dimensional lattice-gases characterised by a
gradient condition which guarantees the existence of Gibbs-type homogeneous
stationary states. We show how, defining appropriate boundary conditions, this
leads to a special symmetry of the system under time and space reversal which,
rephrased in terms of the large deviations function of stationary currents of
conserved quantities, yields a novel fluctuation relation under reservoir
exchange, unrelated to the Gallavotti-Cohen symmetry. We then show that this
relation can be interpreted as a nonequilibrium and nonlinear generalisation
Einstein's relation, leading to Onsager reciprocity relations in the limit of a
small reservoir imbalance. Finally, we illustrate our results with two
examples.
