Brownian motion approach to the ideal gas of relativistic particles

TL;DR

This paper develops a relativistic extension of Brownian motion theory, explicitly deriving relaxation characteristics for velocity and momentum, revealing how thermal effects influence relaxation times in relativistic particles.

Contribution

It introduces a relativistic generalization of Brownian motion and explicitly calculates relaxation times, highlighting the impact of thermal corrections on these processes.

Findings

Thermal corrections slow down relaxation processes.

Transient velocity relaxation time is independent of temperature.

Relaxation times are proportional to initial energy of particles.

Abstract

The relativistic generalization of a free Brownian motion theory is presented. The global characteristics of the relaxation are {\it explicitly} found for the velocity and momentum (stochastic) kinetics. It is shown that the thermal corrections, to the both relaxation times $T$ (of stationary autocorrelations) and transient relaxation time of momentum, appear slowing down the processes. The transient relaxation time of the velocity does not depend {\it explicitly} on temperature, $T(v_0)= m(v_0)/\gamma \equiv \epsilon_0/\gamma c^2$, and it is proportional to the initial energy of a relativistic Brownian particle.