Thermal equilibrium and statistical thermometers in special relativity

TL;DR

This study uses relativistic molecular dynamics simulations to determine the correct velocity distribution in special relativity, confirming the Juettner distribution and clarifying the concept of temperature in relativistic systems.

Contribution

The paper provides the first definitive numerical evidence favoring the Juettner distribution as the relativistic velocity distribution and clarifies the conditions for defining temperature in special relativity.

Findings

Juettner distribution is confirmed as the correct relativistic velocity distribution.

Thermal equilibrium in special relativity requires spatial confinement.

Temperature can be defined and measured independently of observer frame.

Abstract

There is an intense debate in the recent literature about the correct generalization of Maxwell's velocity distribution in special relativity. The most frequently discussed candidate distributions include the Juettner function as well as modifications thereof. Here, we report results from fully relativistic one-dimensional (1D) molecular dynamics (MD) simulations that resolve the ambiguity. The numerical evidence unequivocally favors the Juettner distribution. Moreover, our simulations illustrate that the concept of 'thermal equilibrium' extends naturally to special relativity only if a many-particle system is spatially confined. They make evident that 'temperature' can be statistically defined and measured in an observer frame independent way.