Equilibrium long-range features in a local driven model


  Or Cohen  ,  Adina Lederhendler  ,  David Mukamel  
Department of Physics of Complex Systems, Weizmann Institute of Science

Equilibrium system with long-range interactions exhibit unique features such as inequivalence of statistical ensembles and phase transition in one dimension. Such features are discussed in the context of a driven model with local dynamics, which in general relaxes to a nonequilibrium steady state. The ABC model is a stochastic model where three species of particle hop on ring with asymmetric rates. For the special case where the densities of each species are equal, the model obeys detailed balance with respect to an effective Hamiltonian with long-range interactions, although the dynamics is strictly local. Using this Hamiltonian, the phase diagram of the model is analyzed, showing features that are common to equilibrium system with long-range interactions such as inequivalence of the canonical and grand-canonical ensembles. A dynamical analysis reveals a similar phase diagram even when the densities of each species are not equal, yielding a nonequilibrium steady state with nonvanishing currents of particles. This suggests a possible similarity between nonequilibrium systems and equilibrium systems with long-range interactions.