Entropic formulation of relativistic continuum mechanics

TL;DR

This paper develops an entropic approach to relativistic continuum mechanics, introducing two spatial scales and a local entropy functional, enabling the treatment of various relativistic materials within a unified framework.

Contribution

It presents a novel entropic formulation for relativistic continuum mechanics that incorporates multiple spatial scales and derives dissipative dynamics from entropy maximization.

Findings

Successfully models relativistic viscous fluids.

Extends to relativistic viscoelastic materials.

Provides a unified variational framework for relativistic materials.

Abstract

An entropic formulation of relativistic continuum mechanics is developed in the Landau-Lifshitz frame. We introduce two spatial scales, one being the small scale representing the linear size of each material particle and the other the large scale representing the linear size of a large system which consists of the material particles and is to linearly regress to the equilibrium. We propose a local functional which is expected to represent the total entropy of the larger system and require the entropy functional to be maximized in the process of linear regression. We show that Onsager's original idea on linear regression can then be realized explicitly as current conservations with dissipative currents in the desired form. We demonstrate the effectiveness of this formulation by showing that one can treat a wide class of relativistic continuum materials, including standard relativistic viscous fluids and relativistic viscoelastic materials.