Derivation of Hydrodynamics from the Hamiltonian description of particle systems

Abstract

Hamiltonian particle systems may exhibit non-linear hydrodynamic phenomena as the time evolution of the density fields of energy, momentum, and mass. In this Letter, an exact equation describing the time evolution is derived assuming the local Gibbs distribution at initial time. The key concept in the derivation is an identity similar to the fluctuation theorems. The Navier-Stokes equation is obtained as a result of simple perturbation expansions in a small parameter that represents the scale separation.

7 pages. Minor revisions are made in ver.2; In ver.3, the presentation has been revised substantially, and this version will be published in Phys. Rev. Lett

References in corpus (4)

• Steady State Thermodynamics for Heat Conduction -- Microscopic Derivation
• Possible extended forms of thermodynamic entropy
• Universal description of viscoelasticity with foliation preserving diffeomorphisms
• A glimpse of fluid turbulence from the molecular scale

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