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.
Transport, collective motion, and brownian motion.Progress of theoretical physics, 33(3):423–455
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The orthogonal dynamics for Mori's projection is a strongly continuous semigroup generated by QL Q, with the GLE and 2FDT holding for autonomous systems whose evolution is a strongly continuous semigroup
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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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On the generalized Langevin equation and the Mori projection operator technique
The orthogonal dynamics for Mori's projection is a strongly continuous semigroup generated by QL Q, with the GLE and 2FDT holding for autonomous systems whose evolution is a strongly continuous semigroup