after some research, there are a few different approaches. and the definition of 'zombie' varies.
For starters zombies, like any other thing that causes itself to move, need energy. and so if they dont have a functioning digestive system they would eventually run out of energy. this is the second law of thermodynamics or something.
the marvel explanation of zombies is that they become super efficient and dont need nearly as much energy as people do, so they can live on whatever energy stores they had before their digestive system shut down / was eaten/ fell out/ whatever.
the hyper fast zombies i was thinking of came from some movie i saw, but i cant remember which. theyre the world war z / i am legend zombies (which ive learned are very different). The I am legend zombies are apparantly more of a vampire variation, and the world war z zombies have that fast change and super aggresive zombie style. 28 days later is the same. My impression was that they are super aggresive because all of their bodily functions have been turned way up, so they need more food and burn it off, which would lead to a possible conclusion that they do not have any waste left to poop.
so if you want to believe that walking dead / new definiton of zombies can voilate the laws of physics then fine, but then you may as well resort to the oldschool idea of zombies which is that they were magical like mummys and vampires and could just move around however the fuck they wanted to.