What I've heard seemed to indicate that, if you assigned a certain entropy density function to classical configuration space, and integrated it over a certain area to get entropy at the initial time, then let the area evolve, and integrated over that area to get the entropy at the final time, the entropy would stay constant.

This would mean that conservation of entropy is the actual physical process. Increase in entropy is just us increasing the size at the final time because we're not paying close enough attention to exactly where it should be.

Also, the more you know about the system, the smaller the area you could give in configuration space to specify it, and thus the lower the entropy.

Is this accurate at all?