Relational Composition of Physical Systems: A Categorical Approach

Abstract

Applied category theory is a field of mathematics that has opened up over the last decade and provides new ideas for how to formalize the composition of systems within science and engineering. In this thesis, we take methods from applied category theory and use them to formalize the composition of two types of systems: thermostatic systems and port-Hamiltonian systems. Thermostatic systems are a simplification of thermodynamic systems, retaining only the information necessary to discuss equilibria. Port-Hamiltonian systems are a generalization of classical mechanical systems that allow for energy to flow in and out of a system. The theory we use to formalize the composition of both of these systems is the theory of operads and operad algebras, and we hope to demonstrate that this theory has rich application beyond our use of it, and thus is a promising future point of study.