Abstract

We examine a class of one-dimensional lattice-gases characterised by a gradient condition which is a necessary and sufficient condition for the existence of Gibbs-type homogeneous stationary states. We show how, defining appropriate boundary conditions, this condition leads to a novel fluctuation relation under reservoir exchange, unrelated to the Gallavotti–Cohen symmetry. We show that it can be interpreted as a nonequilibrium and nonlinear generalisation of Einstein’s relation, leading to Onsager reciprocity relations in the limit of a small reservoir imbalance. We illustrate these results with two examples.

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