# Statistical Mesoscopic Hydro-Thermodynamics: The Description of Kinetics and Hydrodynamics of Nonequilibrium Processes in Single Liquids

## TL;DR

This paper introduces mesoscopic hydro-thermodynamics, a higher-order generalized hydrodynamics framework that describes fluid motion at intermediate scales using densities and fluxes of all orders, incorporating Maxwell-like times for accurate characterization.

## Contribution

It develops a mesoscopic hydro-thermodynamics framework based on a statistical formalism, extending previous models to include higher-order fluxes and their associated times for nonequilibrium processes.

## Key findings

- Provides a formalism for describing fluid motion at mesoscopic scales.
- Incorporates Maxwell-like times to determine the relevant fluxes.
- Extends previous hydrodynamics models to include higher-order effects.

## Abstract

Hydrodynamics, a term apparently introduced by Daniel Bernoulli (1700-1783) to comprise hydrostatic and hydraulics, has a long history with several theoretical approaches. Here, after a descriptive introduction, we present so-called mesoscopic hydro-thermodynamics, which is also referred to as higher-order generalized hydrodynamics, built within the framework of a mechanical-statistical formalism. It consists of a description of the material and heat motion of fluids in terms of the corresponding densities and their associated fluxes of all orders. In this way, movements are characterized in terms of intermediate to short wavelengths and intermediate to high frequencies. The fluxes have associated Maxwell-like times, which play an important role in determining the appropriate contraction of the description (of the enormous set of fluxes of all orders) necessary to address the characterization of the motion in each experimental setup. This study is an extension of a preliminary article: Physical Review E \textbf{91}, 063011 (2015).