Entropy never comes into it because we are not talking about a closed system. So long as a creature can eat food, or synthesize it from the sun's rays, they are

Entropy never comes into it because we are not talking about a closed system. So long as a creature can eat food, or synthesize it from the sun's rays, they are an open system taking in substances that give it fresh energy. You could model this a few ways. You could say a creature exports its entropy by eating food, or you could say, more accurately, that the entropy was created when the energy was stored in chemical form in whatever substances the creature eats. If there was some ultimate limit on the ability of creatures to communicate information forward then the aging process would apply to the entire species, to life itself, rather than to individual organisms. You can think of yourself as an organism that was created a few years ago by your mother and father, but as a chemical process, you are 4 billion years old, give or take a few hundred million years. There has not been a single second, in the last 4 billion years, when the chemical reaction that is you was not working to propagate itself forward. If entropy applied to you, then surely you would not have lasted 4 billion years?