A century after Ising introduced the Ising measure to study equilibrium systems, its relevance has expanded well beyond equilibrium contexts, notably appearing in nonequilibrium frameworks such as the Katz-Lebowitz-Spohn (KLS) model. In this work, we investigate a class of generalized asymmetric simple exclusion processes (ASEPs) for which the Ising measure serves as the stationary state. We show that the average stationary current in these models can display current reversal and other unconventional behaviors, offering insights into transport phenomena in nonequilibrium systems. Moreover, although long-range interaction rates often give rise to long-range interactions in the potential function, our model provides a counterexample: Even with long-range interactions in the dynamics, the resulting potential remains short ranged. Finally, our framework encompasses several well-known models as special cases, including ASEPs, the KLS model, the facilitated exclusion process, the cooperative exclusion process, and the assisted exchange model.

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• Exclusion processes
• Nonequilibrium lattice models