Subsystem symmetries produce nonlinear hydrodynamics preserving marginal distributions, realizing partial multipole conservation with monotonic total correlation decay.
(A1) Taking the functional derivative, we have δS δρ =−log ρ(x, y) q −1−λ−ϕ x(x)−ϕ y(y) = 0, (A2) which gives us ρ(x, y) =e lnq−1−λ−ϕ x(x)−ϕy(y)
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Diffusion with conserved marginal distributions and information theory in fracton hydrodynamics
Subsystem symmetries produce nonlinear hydrodynamics preserving marginal distributions, realizing partial multipole conservation with monotonic total correlation decay.