Statistical mechanics of Euler equations in two dimensions

Abstract

We formulate the statistical mechanics of a two-dimensional inviscid incompressible fluid in a manner which, for the first time, respects all conservation laws. For a special case, we demonstrate that a mean-field theory is exact. A consequence of our arguments is that, in an inviscid fluid evolving from initial conditions to statistical equilibrium, only the energy and certain one-body integrals appear to be conserved. Our methods may be applied to a variety of Hamiltonian systems possessing an infinite number of conservation laws.