Morrey's Derivation of Hydrodynamics from Statistical Mechanics: A Modern Exposition

Abstract

This paper is a modern review of C. B. Morrey's 1955 paper on the derivation of the equations of hydrodynamics from statistical mechanics. It has two main parts. First, assuming the existence of certain invariant N -particle phase distributions, Morrey derives formal balance laws for mass, momentum, and energy. Second, he attempts to construct a concrete sequence of such distributions by imposing cell-wise constraints that match the prescribed macroscopic fields (\r{ho}, u, e). From this construction, he obtains a Gibbs-type limiting form and finally the Euler equations. Compared to classical results, this regime employs the scaling law of N\epsilon^3 = O(1) and leads to a more flexible pressure Peq . Our goal is to explain what Morrey is trying to do, why it's natural and where its most delicate points lie. We will rewrite the argument in a more transparent way, distinguishing carefully between formal derivations, physical input, and statements that still need justification.