Thermal fluctuations propagation in the relativistic Euler regime: a causal appraisal

TL;DR

This paper demonstrates that thermal fluctuations in a relativistic fluid obey a wave equation in the Euler regime, with propagation speeds that reduce to the classical speed of sound in the non-relativistic limit, offering insights into relativistic fluid dynamics.

Contribution

It shows that thermal fluctuations in a relativistic fluid satisfy a wave equation and calculates their propagation speeds, providing a causal analysis of fluctuation propagation.

Findings

Thermal fluctuations obey a wave equation in the relativistic Euler regime.

Propagation speeds are explicitly calculated and match classical sound speed in the non-relativistic limit.

Implications for relativistic fluid dynamics are discussed.

Abstract

It is shown that thermal fluctuations present in a simple non-degenerate relativistic fluid satisfy a wave equation in the Euler regime. The characteristic propagation speeds are calculated and the classical expression for the speed of sound is recovered at the non relativistic limit. Implications and generalizations of this work are analyzed.