Physical completion of the Navier-Stokes equations (opens in new tab)

The incompressible Navier-Stokes equations contain viscous dissipation but no thermal noise. I show, using a topological argument based on Poincar\'e's lemma, that the fluctuation-dissipation relation for the full nonlinear dynamics can be derived without the linearisation or structural assumptions that all previous derivations require. The nonlinear convective term is Hamiltonian (energy-preserving and phase-space-volume-preserving) and drops o...