Seriously. There's precisely nothing useful here. It's one giant mess of seriously flawed interpretations of the First Law. Think about it. What happens to this lost fat between the moment it's released from fat tissue and the moment it's exhaled? Let me rephrase. What happens to gasoline between the moment it leaves the gas tank and the moment it's exhausted? It's converted. Converted to what? Work. Same thing happens to "lost" fat. It ain't lost, it's used. In fact, conversion is work. In an internal combustion engine for example, gasoline is combined with air, ignited in the combustion chamber which is sealed, combustion produces heat and pressure, this pressure has no place to go so the piston moves, this in turn moves the connecting rod, the crankshaft, the transmission, the wheels, the car moves. Work was produced directly from the conversion of gasoline/air into its elements, from mass to mass. No mass was destroyed nor created in the conversion, yet work was produced. In fact, the opposite conversion that produced the gasoline in the first place required work. When we burn gas in our cars, we're merely extracting this work. Thus, when we're converting fat to CO2 and H2O, we're extracting the work that went into converting CO2 and H2O into fat in the first place.

Thus, the real question ain't what happens to fat when we lose it, but what happens to work when we convert fat back to its elements. That physicist needs a refresher course.