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The question is whether driven systems have a similar quantity that equalizes on contact, independent of how they touch.","posed_since":"2006","precise":"For two driven lattice gases (e.g., driven exclusion processes or the Katz-Lebowitz-Spohn model) exchanging particles through a weak contact, determine whether an intensive variable defined from each isolated steady state, such as the chemical potential of Sasa-Tasaki steady-state thermodynamics, predicts the joint stationary densities to leading order in the contact rate, independent of the contact dynamics. Answer: yes with the construction, or a class of counterexamples.","problem_ref":null,"references":"","settled_by":"An exact solution or proof for a pair of driven lattice gases showing whether the joint state is fixed by single-system intensive variables.","status_note":"Simulations of driven lattice gases show contact-dependent violations for some definitions, while consistency holds in specific weak-contact limits.","title":"Zeroth law for two driven systems in weak 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