# Multiscale Theory

## TL;DR

This paper develops an abstract framework connecting various mesoscopic dynamical theories through a generalized time evolution equation based on the Boltzmann kinetic equation, highlighting links and open problems.

## Contribution

It introduces a novel abstract formulation of the Boltzmann kinetic equation connecting different mesoscopic theories and discusses related open problems.

## Key findings

- Unified framework for mesoscopic theories
- Representation of kinetic equations as abstract evolution equations
- Identification of open research questions

## Abstract

Boltzmann kinetic equation is put into the form of an abstract time evolution equation representing links connecting autonomous mesoscopic dynamical theories involving varying amount of details. In the chronological order we present results that led to the abstract time equation evolution in both state space and the space of vector fields. In the final section we list some open problems.