{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"7f490f796626ee6f7da76e7943e621a31aa8813efdffff2c26454c61b4e57b0a","created":"2026-10-03T07:18:11Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"9a31193f04ce1d05a29e95774fb078a367cf7d9632f75f58b6646ca8def4d016","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"stat.nonequilibrium-steady-states.additivity-principle-breakdown","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"Large current fluctuations in a driven conductor can be computed from a principle that assumes the most likely fluctuation keeps a fixed density profile in time. For some systems and currents the most likely fluctuation instead changes its profile in time or breaks a symmetry of the system, which is a phase transition in the fluctuations.","posed_since":"2004","precise":"For one-dimensional boundary-driven diffusive systems described by macroscopic fluctuation theory with diffusivity $D(\\rho)$ and mobility $\\sigma(\\rho)$, classify the ($D, \\sigma$, boundary densities, current $j$) for which the large deviation function of the time-integrated current is given by the time-independent additivity-principle solution, and where time-dependent optimal paths (traveling waves on a ring) or symmetry-broken time-independent profiles take over. An answer is a necessary and sufficient criterion.","problem_ref":null,"references":"","settled_by":"A proof of a necessary and sufficient condition within macroscopic fluctuation theory, checked against exact results for the KMP and exclusion models.","status_note":"Sufficient conditions for stability of the additivity solution and explicit violations are known, including symmetry-breaking transitions in boundary-driven systems (Baek, Kafri, Lecomte, Phys. Rev. Lett. 118, 030604, 2017); a general criterion is not.","title":"When the additivity principle fails for current 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