Radon transform and kinetic equations in tomographic representation

TL;DR

This paper explores the use of the Radon transform to reformulate kinetic equations in a tomographic framework, linking phase space densities with tomographic probabilities, and applies this to classical systems like Liouville equations.

Contribution

It introduces a novel tomographic representation of kinetic equations using the Radon transform, providing new insights into classical statistical processes.

Findings

Tomographic form of kinetic equations is constructed.

Relation between phase space densities and tomographic probabilities is clarified.

Applications to Liouville equations demonstrate the approach.

Abstract

Statistical properties of classical random process are considered in tomographic representation. The Radon integral transform is used to construct the tomographic form of kinetic equations. Relation of probability density on phase space for classical systems with tomographic probability distributions is elucidated. Examples of simple kinetic equations like Liouville equations for one and many particles are studied in detail.