Probability measures on the path space and the sticky particle system

TL;DR

This paper introduces a probabilistic framework for modeling sticky particle systems in one dimension, providing a novel method to construct solutions with nonincreasing kinetic energy and entropy conditions.

Contribution

It develops a new approach to associate probability measures with particle paths, enabling the design of solutions that conserve energy properties and satisfy entropy inequalities.

Findings

Established a measure-theoretic description of particle sticking behavior.

Provided a new solution construction method for the sticky particle system.

Demonstrated solutions with nonincreasing kinetic energy and entropy compliance.

Abstract

We study collections of point masses which move freely along the real line and stick together when they collide via perfectly inelastic collisions. We quantify the way particles stick together and explain how to associate a probability measure on the space of continuous paths to such a collection of evolving point masses. These observations lead to a new method of designing solutions to the sticky particle system in one spatial dimension which have nonincreasing kinetic energy and satisfy an entropy inequality.