Contrasting thermodynamic and hydrodynamic entropy

TL;DR

This paper compares thermodynamic and hydrodynamic entropy in turbulence and other systems, highlighting their differences and non-additivity, with implications for understanding multiscale disorder.

Contribution

It introduces the concept of hydrodynamic entropy and analyzes its properties, contrasting it with thermodynamic entropy in various physical models.

Findings

Hydrodynamic entropy is not extensive and not proportional to system size.

Hydrodynamic and thermodynamic entropies cannot be simply added due to their different scales.

The paper discusses hydrodynamic entropy in Ginzburg-Landau and Ising models.

Abstract

In this paper, using \textit{hydrodynamic entropy} we quantify the multiscale disorder in Euler and hydrodynamic turbulence. These examples illustrate that the hydrodynamic entropy is not extensive because it is not proportional to the system size. Consequently, we cannot add hydrodynamic and thermodynamic entropies, which measure disorder at macroscopic and microscopic scales, respectively. In this paper, we also discuss the hydrodynamic entropy for the time-dependent Ginzburg-Landau equation and Ising spins.