I'm a physicist, and I roll my eyes whenever anyone starts up with simplistic arguments about humans, food, and thermodynamics. Thermodynamics holds, but the system doesn't work the way you think it does.
Other things that can happen when your metabolism slows down are that you get tired more often and more easily, your thought processes slow down, you sleep more. This happens to everyone as they age, and it can also happen from chronic stress, calorie restriction sufficient to trigger 'starvation mode', and anything else that causes your body to try to conserve energy for survival.
Most people in the thread here seem to be saying your body will find a way to use the same amount of energy, and store the same amount of energy, despite the energy intake being different.
Anecdotally, I've lost over 10 kg while not caring about aspartame intake (in fact I think it probably went up).