I just have read about the law of maximum entropy production. Someone has idolized it enough to make a whole website just for it: http://www.lawofmaximumentropyproduction.com/

A system will select the path or assemblage of paths out of available paths that minimizes the potential or maximizes the entropy at the fastest rate given the constraints

Isn't this exactly how the principle of least action works? I know that the two are different, one is applied in microscopic and one in macroscopic, but without looking to its root, they are the similar to each other. It is surprisingly that there is no article about the similarity between this, or at least I couldn't find one. Do you have any idea about this?