# Multiscale thermodynamics of charged mixtures

## TL;DR

This paper develops a comprehensive multiscale thermodynamic framework for charged fluid mixtures, integrating continuum mechanics, electrodynamics, and thermodynamics using geometric and Hamiltonian methods, with applications to engineering models.

## Contribution

It introduces a novel multiscale theory combining geometric mechanics and thermodynamics for charged mixtures, unifying reversible and irreversible processes within the GENERIC framework.

## Key findings

- Derived a new Poisson bracket for the Hamiltonian system.
- Implemented gradient dynamics for irreversible thermodynamics.
- Recovered standard engineering models as low-level limits.

## Abstract

A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely geometric way by means of semidirect products. This leads to a complex Hamiltonian system with a new Poisson bracket, which can be used in principle with any energy functional. The thermodynamic (irreversible) part is added as gradient dynamics, generated by derivatives of a dissipation potential, which makes the theory part of the GENERIC framework. Subsequently, Dynamic MaxEnt reductions are carried out, which lead to reduced GENERIC models for smaller sets of state variables. Eventually, standard engineering models are recovered as the low-level limits of the detailed theory. The theory is then compared to recent literature.