# A minimum entropy principle in the compressible multicomponent Euler equations

## TL;DR

This paper investigates the admissible entropy functions for the compressible multicomponent Euler equations and establishes a minimum entropy principle applicable to both smooth and discrete entropy solutions.

## Contribution

It extends the minimum entropy principle to multicomponent Euler equations by characterizing the entropy functions and proving the principle holds for all entropy solutions.

## Key findings

- Established the space of admissible entropy functions.
- Proved the minimum entropy principle for smooth and discrete solutions.
- Extended classical results to multicomponent systems.

## Abstract

In this work, the space of admissible entropy functions for the compressible multicomponent Euler equations is explored, following up on [Harten, \textit{J. Comput. Phys.}, 49 (1), 1983, pp. 151-164]. This effort allows us to prove a minimum entropy principle on entropy solutions, whether smooth or discrete, in the same way it was originally demonstrated for the compressible Euler equations by [Tadmor, \textit{Appl. Numer. Math.}, 49 (3-5), 1986, pp. 211-219].