Thermodynamics and Hydrodynamics (Statistical Foundations): 1. The Problem Setup

Analyzing the physical foundations of statistical mechanics, we show that it can only be local. This means that the structure of matter and all its macroscopic parameters (except the density ρ, the velocity \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\overrightarrow v$$ \end{document} of the liquid, and the temperature θ) must be determined by what occurs inside a correlation sphere of the radius R≈10−7cm; the values of ρ, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\overrightarrow v$$ \end{document}, and θ, which play the role of fixed parameters for the BBGKY hierarchy, must be found by solving hydrodynamic equations with macroscopic boundary and initial conditions taken into account.