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Résumé |
Gianni Jona-Lasinio and his collaborators have proposed in the early 2000's a non-linear
action functional that encodes the macroscopic fluctuations and the large deviations for a
wide class of diffusive systems out of equilibrium. In this Macroscopic Fluctuation Theory
(MFT), optimal fluctuations far from equilibrium can be found, at a coarse-grained scale, by
solving two coupled non-linear hydrodynamic equations.
In this talk, we shall show that the MFT equations for the symmetric exclusion process are
classically integrable and can be solved with the help of the inverse scattering method,
originally developed to study solitons in the KdV or the NLS equations. This exact solution
will allow us to calculate the large deviations of the current and the optimal profiles that
generates a given fluctuation, both at initial and final times. This macroscopic solution
matches previous results that were derived, by applying the Bethe Ansatz, at the microscopic
level.
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