When the additivity principle fails for current fluctuations · revision history

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Title

When the additivity principle fails for current fluctuations

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.

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.

Settled by

A proof of a necessary and sufficient condition within macroscopic fluctuation theory, checked against exact results for the KMP and exclusion models.

Kind

well-posed

Answer type

classification

References

(empty)

Literature status

partially-resolved

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.

Posed since

2004