Causal diffusions, causal Zeno effect and collision number

TL;DR

This paper investigates diffusion processes, including relativistic particles, revealing a causal Zeno effect and proposing a lognormal distribution for collision numbers based on numerical results.

Contribution

It introduces a causal Zeno effect analogy in diffusion processes and models the collision number distribution as lognormal, supported by numerical evidence.

Findings

Identification of a causal Zeno effect in relativistic diffusion.

Proposal of a lognormal distribution for collision numbers.

Numerical support for the distribution model.

Abstract

We consider diffusion processes with the help of Markov random walk models. Especially the process of diffusion of a relativistic particle in a relativistic equilibrium system is considered. We interpret one of the results as causal Zeno effect for its similarity to quantum Zeno effect. Another problem we considered is about collision number. Basing on our numerical results, we propose that in the considered situation the probability density distribution among different collision numbers is a lognormal distribution.