Explicit large-deviation function for the SSEP with a battery

Derive explicit expressions for the large-deviation function of the current and the current generating function of the symmetric simple exclusion process on a ring with a battery for arbitrary current and counting-field values.

Background

The paper applies macroscopic fluctuation theory to the symmetric simple exclusion process (SSEP) on a ring containing a special link that acts as a battery. The theory yields the current large-deviation function and generating function in parametric form through an optimization over density profiles and boundary densities.

Although the authors obtain explicit formulas for selected regimes, including half filling and a fully directed battery, they do not obtain closed-form expressions valid for arbitrary current or counting-field values. Thus, an unresolved problem is to convert the parametric MFT characterization into explicit formulas for the general SSEP-with-battery setting.

References

Even for the SSEP we did not succeed to obtain more explicit expressions of these quantities for arbitrary $q$ or $\lambda$.

— Current fluctuations of diffusive systems with a battery  (2609.18851 - Jonckheere et al., 16 Sep 2026) in Section 4, subsection “The symmetric exclusion process with a battery”

but we do not have at the moment any explanation for this apparent power law convergence.

— Current fluctuations of diffusive systems with a battery  (2609.18851 - Jonckheere et al., 16 Sep 2026) in Section 4, subsection “Convergence of the results”