On Kinetic Equations for Collisional Dynamics of Active Soft Condensed Matter

TL;DR

This paper introduces a novel kinetic equation framework for modeling the collective behavior of biological systems, emphasizing a direct observable-based approach over traditional state-based methods.

Contribution

It proposes a new observable evolution equation approach that offers a fully consistent mathematical model for biological collective dynamics, diverging from traditional kinetic theory.

Findings

Develops a new kinetic equation formulation for biological systems

Provides a mathematically consistent model for collective behavior

Highlights the limitations of traditional state-based kinetic descriptions

Abstract

We consider a new approach to the description of the collective behavior of complex systems of mathematical biology based on the evolution equations for observables of such systems. This representation of the kinetic evolution seems, in fact, the direct mathematically fully consistent formulation modeling the collective behavior of biological systems since the traditional notion of the state in kinetic theory is more subtle and it is an implicit characteristic of the populations of living creatures.