The answer is way more complicated than you think. The short answer is: of course not, thermodynamics says that if you consume/burn the exact same amount of energy that’s all there is.
The longer answer is that before ketosis you deplete all your carb stores due to your body’s preference for them. Once they are all gone, you have lower glycogen and blood glucose levels (your carb stores) so your only option is to metabolize body fat and/or lipoproteins in blood. So you may burn more fat as a fuel source, but you don’t burn any extra *calories*.
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