Non-perturbative hydrodynamic limits: A case study

• We introduce a non-perturbative approach to derive hydrodynamics from kinetics.
• Schwinger–Dyson equation for the slow invariant hydrodynamic manifold is derived.
• Exact invariant manifold is found for a model kinetic equation.
• Exact diffusion mode is constructed.
• Comparison to the Chapman–Enskog expansion is presented.

We introduce non-perturbative analytical techniques for the derivation of the hydrodynamic manifolds from kinetic equations. The new approach is analogous to the Schwinger–Dyson equation of quantum field theories, and its derivation is demonstrated with the construction of the exact diffusion manifold for a model kinetic equation.