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.
Statistical mechanics of irreversibility.Quantum Statistical Mechanics, page 139, 1966
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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.