Weakly Non-Equilibrium Properties of Symmetric Inclusion Process with   Open Boundaries
  We study close to equilibrium properties of the one-dimensional Symmetric Inclusion Process (SIP) by coupling it to two particle-reservoirs at the two boundaries with slightly different chemical potentials. The boundaries introduce irreversibility and induce a weak particle current in the system. We calculate the McLennan ensemble for SIP, which corresponds to the entropy production and the first order non-equilibrium correction for the stationary state. We find that the first order correction is a product measure, and is consistent with the local equilibrium measure corresponding to the steady state density profile. 
Kiamars Vafayi and Manh Hong Duong
math-ph cond-mat.stat-mech math.MP math.PR