In integrable one-dimensional systems hydrodynamic noise vanishes according to a projected Kubo formula, yielding a ballistic macroscopic fluctuation theory that describes all-order hydrodynamics.
Fluctuation renormalization in nonlinear dynamics.Progress of Theo- retical Physics, 55(2):430–437
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Hydrodynamic noise in one dimension: projected Kubo formula and how it vanishes in integrable models
In integrable one-dimensional systems hydrodynamic noise vanishes according to a projected Kubo formula, yielding a ballistic macroscopic fluctuation theory that describes all-order hydrodynamics.