Relativistic theory of the viscosity of fluids across the entire energy spectrum

TL;DR

This paper develops a comprehensive relativistic theory of fluid viscosity that unifies classical and ultrarelativistic regimes, revealing a relativistic enhancement mechanism and providing new analytical formulas for hot dense matter and quark-gluon plasma.

Contribution

It introduces a relativistic framework for fluid viscosity based on the Langevin equation and linear response theory, extending classical results and deriving new formulas for ultrarelativistic fluids.

Findings

The theory recovers classical viscosity dependencies in the non-relativistic limit.

It uncovers a relativistic enhancement mechanism of viscosity.

Provides a new analytical formula for viscosity in ultrarelativistic fluids.

Abstract

The shear viscosity is a fundamental transport property of matter. Here we derive a general theory of the viscosity of gases based on the relativistic Langevin equation (deduced from a relativistic Lagrangian) and nonaffine linear response theory. The proposed relativistic theory is able to recover the viscosity of non-relativistic classical gases, with all its key dependencies on mass, temperature, particle diameter and Boltzmann constant, in the limit of Lorentz factor $\gamma=1$. It also unveils the relativistic enhancement mechanism of viscosity. In the limit of ultrarelativistic fluids, the theory provides a new analytical formula which reproduces the cubic increase of viscosity with temperature in agreement with various estimates for hot dense matter and the QGP-type fluid.