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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Time parameters and Lorentz transformations of relativistic stochastic processes.

Jörn Dunkel¹, Peter Hänggi, Stefan Weber

¹Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, United Kingdom. jorn.dunkel@physics.ox.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|March 5, 2009

Summary

This study derives rules for time parameter transformations in relativistic Langevin equations. It reveals that coordinate-time processes approaching the Jüttner-Maxwell distribution lead to modified momentum distributions in proper time.

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Area of Science:

Relativistic statistical mechanics
Theoretical physics

Background:

Relativistic Langevin equations describe particle dynamics in relativistic systems.
The Jüttner-Maxwell distribution is a key concept in relativistic kinetic theory.

Purpose of the Study:

To derive and discuss rules for time parameter transformations in relativistic Langevin equations.
To investigate the relationship between coordinate-time and proper-time parametrizations.

Main Methods:

Derivation of transformation rules for time parameters.
Analysis of the convergence of parametrized processes.

Main Results:

Established rules for time parameter transformations in relativistic Langevin equations.
Demonstrated that coordinate-time processes approaching the Jüttner-Maxwell distribution yield modified proper-time momentum distributions.
Identified a factor proportional to the inverse energy characterizing this modification.

Conclusions:

The choice of time parameter significantly impacts momentum distribution in relativistic systems.
This work provides a theoretical framework for understanding time parameter effects in relativistic statistical mechanics.