The metric in sub-Riemannian geometry is often called the Carnot-Carathéodory metric.
Question 1. What is the origin of this name? Who was the first to introduce it?
I believe that the "Carathéodory" part of the name could be related to his work in theoretical thermodynamics , but I do not really know how it is related to his work.
Question 2. How is the notion of Carnot-Carathéodory metric related to the work of Carathéodory?
I know that Carnot groups are special examples of sub-Riemannian manifolds, but is it the reason for "Carnot" part in the name of the metric?
Question 3. What does the "Carnot" part of the name of the metric stand for?
 C. Carathéodory, Untersuchungen uber die Grundlagen der Thermodynamik. Math. Ann. 67 (1909), 355–386.