Shape-Dependent Thermodynamics and Non-Local Hydrodynamics in a   Non-Gibbsian Steady-State of a Drift-Diffusion System
  Shape-dependent thermodynamics and non-local hydrodynamics are argued to occur in dissipative steady states of driven diffusive systems. These predictions are confirmed by numerical simulations. Unlike power-law correlations, these phenomena cannot be explained by a hypothesis of ``criticality''. Instead, they require the effective Hamiltonian of the system to contain very long-range potentials, making the invariant probability measures formally ``non-Gibbsian''. 
Francis J. Alexander (Boston University) and Gregory L. Eyink   (University of Arizona)