Relational Composition of Physical Systems: A Categorical Approach

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.