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We study close to equilibrium properties of the one-dimensional SymmetricInclusion Process (SIP) by coupling it to two particle-reservoirs at the twoboundaries with slightly different chemical potentials. The boundariesintroduce irreversibility and induce a weak particle current in the system. Wecalculate the McLennan ensemble for SIP, which corresponds to the entropyproduction and the first order non-equilibrium correction for the stationarystate. We find that the first order correction is a product measure, and isconsistent with the local equilibrium measure corresponding to the steady statedensity profile.

Weakly Non-Equilibrium Properties of Symmetric Inclusion Process with Open Boundaries