Stationarity, soft ergodicity, and entropy in relativistic systems

TL;DR

This paper explores how different time-parameterizations affect stationarity, ergodicity, and entropy in relativistic systems, using molecular dynamics simulations to understand these phenomena within a deterministic framework.

Contribution

It demonstrates how relativistic effects on ergodicity and entropy depend on time-parameterizations, linking these concepts within a deterministic model system.

Findings

Different time-parameters lead to distinct types of soft ergodicity.

Relativistic entropy is closely connected to the choice of time-parameterization.

Simulations combining molecular dynamics with stochastic processes can benefit from this understanding.

Abstract

Recent molecular dynamics simulations show that a dilute relativistic gas equilibrates to a Juettner velocity distribution if ensemble velocities are measured simultaneously in the observer frame. The analysis of relativistic Brownian motion processes, on the other hand, implies that stationary one-particle distributions can differ depending on the underlying time-parameterizations. Using molecular dynamics simulations, we demonstrate how this relativistic phenomenon can be understood within a deterministic model system. We show that, depending on the time-parameterization, one can distinguish different types of soft ergodicity on the level of the one-particle distributions. Our analysis further reveals a close connection between time parameters and entropy in special relativity. A combination of different time-parameterizations can potentially be useful in simulations that combine molecular dynamics algorithms with randomized particle creation, annihilation, or decay processes.