Zeroth law for two driven systems in weak contact
In plain words
Two systems in equilibrium that exchange particles stop exchanging on average when their chemical potentials are equal. The question is whether driven systems have a similar quantity that equalizes on contact, independent of how they touch.
Precise statement
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.
What would settle it
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 in the literature
Simulations of driven lattice gases show contact-dependent violations for some definitions, while consistency holds in specific weak-contact limits.