Relational Composition of Physical Systems: A Categorical Approach

TL;DR

This thesis develops category-theoretic frameworks for composing physical systems, specifically port-Hamiltonian and thermostatic systems, to better understand their interactions and equilibria.

Contribution

It introduces two novel categorical frameworks for relational composition of physical systems, expanding the mathematical tools for system analysis.

Findings

Frameworks formalize energy flow and entropy-based equilibria

Provides a rigorous categorical foundation for physical system composition

Integrates linear algebra, differential geometry, and convex geometry

Abstract

In this master's thesis, we rigorously develop two frameworks of relational composition of systems using tools from category theory. The first framework addresses port-Hamiltonian systems, which are dynamical systems whose dynamics are connected to flows of energy across a boundary. The second framework addresses thermostatic systems, which are descriptions of equilibria in physical systems using entropy. We also review necessary subjects to develop these frameworks from a category-theoretic viewpoint, including inear algebra, differential geometry, and convex geometry.