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In this note we consider non-equilibrium steady states of one-dimensionalmodels of heat conduction (wealth exchange) which are coupled to somereservoirs creating currents. In particular we will give sufficient andnecessary conditions which will depend only on the first two moments of thereservoir measures and the redistribution parameter under which the two-pointfunctions are multilinear. This presents the first example of multilineartwo-point functions in the absence of product stationary measures.

Multilinearity of two-point correlation functions in one-dimensional models out of equilibrium