Stokes' theorem as an entropy-extremizing duality

Abstract

Given a manifold $\mathcal{M} \subset \mathbb{R}^n$, we consider all codimension-1 submanifolds of $\mathcal{M}$ that satisfy the generalized Stokes' theorem and show that $\partial\mathcal{M}$ uniquely maximizes the associated entropy functional. This provides an information theoretic characterization of the duality expressed by Stokes' theorem, whereby a manifold's boundary is its 'least informative' subset satisfying the Stokes relation.