Monash Open Day in 2020 was a purely online affair, thanks to COVID. I recorded a video talking about Topology: The Shape of Space.
Entropy means many different things in different contexts, but there is a wonderful notion of entropy which is purely topological. It only requires a space, and a map on it. It is independent of geometry, or any other arbitrary features — it is a purely intrinsic concept. This notion is known as topological entropy.