Originally Posted by Teddiursa of the Sky
It isn't a closed system though. You still have sunlight, therefore it breaks no law of thermodynamics. It would take far too long for a zombie to die of "starvation".
Sunlight only works if the Zombie has some way of converting the energy from light (or heat) to ATP, or else some other usable form. Your plants have an entire process for this: there are organelles in almost every plant cell to do this. Viruses (as generally agreed to be the cause of zombieism (zombism?)) do not have enough genetic material to do give the body a mechanism to do this with, ergo the argument about sunlight is invalid.