What you've stated is not a law of thermodynamics. The first law of thermodynamics, which is the one often misused to tell us that calories are the only thing that matter, states that within an isolated system, the total energy of a system is constant. It's well defined. The human body isn't an isolated system, and the laws of thermodynamics aren't tongue in cheek.
Our bodies don't burn calories, and you are right in saying that we do indeed eat food, not calories.
Fasting can, for example, deplete our liver's glycogen stores, and change the levels of various hormones in our body.