# Brownian motion approach to the ideal gas of relativistic particles

Source: [Brownian motion approach to the ideal gas of relativistic particles](<https://www.sota2.com/research/paper/68fa33f11e209131ce894352>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T20:21:03.259Z

Authors: Ryszard Zygad{\\l}o

Published: 2003-10-06T14:32:41.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0310113>)

[PDF](<https://arxiv.org/pdf/cond-mat/0310113.pdf>)