Existence of a thermodynamics for macroscopic driven steady states
In plain words
Equilibrium thermodynamics predicts what happens when systems are put in contact or split into phases using a few numbers such as temperature and chemical potential. Whether driven macroscopic systems have a similar small set of numbers with the same predictive power is unknown.
Precise statement
For driven lattice gases and boundary-driven diffusive systems described by macroscopic fluctuation theory, determine whether intensive variables and a free-energy-like function, defined from isolated steady states (as in Sasa-Tasaki steady-state thermodynamics), predict beyond linear response the outcome of macroscopic operations: contact between systems, phase coexistence, and response to slow changes of parameters. Answer: yes with the construction and its domain, or a no-go result with counterexamples.
What would settle it
A proof that such a construction predicts contact and coexistence for a stated class of driven models, or explicit models in which no single-system variables can do so.
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