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.
Hydrodynamic fluctuations of stochastic charged cellular automata
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Tracer position statistics in single-file hard-rod transport are universal across diffusive and ballistic dynamics for one-time distributions.
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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.
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Universal tracer statistics in single-file transport
Tracer position statistics in single-file hard-rod transport are universal across diffusive and ballistic dynamics for one-time distributions.