Entropy maximizing curves
Revue Roumaine de Mathematiques Pures et Appliquees
The paper defines the entropy of an oval curve as a function of its curvature and finds the ovals with maximum entropy. The problem of finding the entropy maximizing curves between two points is treated using the Lagrangian formalism and solved in closed form. The paper studies also the smooth isometric deformations of the type d t φ t (s) - 1/2d 2s φ t (s) = σ(t) φ t (s) and proves that they are both area and entropy increasing, the oval with the maximum entropy being a circle.
Calin, O. (2018). Entropy maximizing curves. Revue Roumaine de Mathematiques Pures et Appliquees, 63(2), 91–105.