Statistical Fluid Mechanics: Dynamics Equations and Linear Response Theory

TL;DR

This paper introduces a statistical mechanical framework for fluid dynamics that incorporates molecular-level velocity distributions, providing new insights into heat, sound, and motion propagation within fluids.

Contribution

It develops a statistical mechanical approach to fluid mechanics, deriving dynamics equations and applying linear response theory to connect molecular behavior with macroscopic phenomena.

Findings

Heat, sound, and motion are intrinsically linked in statistical fluid dynamics.

The approach provides a foundation for future applications in statistical fluid mechanics.

Green's functions and linear response theory are successfully applied to this framework.

Abstract

The statistical nature of discrete fluid molecules with random thermal motion so far has not been considered in mainstream fluid mechanics based on Navier-Stokes equations, wherein fluids have been treated as a continuum breaking into many macroscopically infinitely small (but microscopically large enough) mass elements with their motion only characterized by center-of-mass velocity. Here we provide a Statistical Mechanical approach to address fluid dynamics by considering statistical velocity distribution of discrete molecules within macroscopically infinitely small volume elements as well as their center-of-mass velocity. Dynamics equations governing the evolution of physical variables have been proposed, Green's functions have been obtained and linear response theory has been applied to study physical situations with external heat perturbation. It is found that the propagation of heat, center-of-mass motion and sound are intrinsically integrated in Statistical fluid dynamics. This work lays down the foundation for applications of Statistical fluid mechanics.