Что значит "running off / running on fumes" ?

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The first sentence meaning of running off is they are burning calories or expending energy (usually it’s said if the person feels the calories of the food they ate was above and beyond a normal caloric intake). Not necessarily digest, but more like “working off” the calories?
The second sentence means that the person is pretty much out of energy and is just functioning on what little energy is left that was provided to him by the chocolate muffin. So yes, he is drained of the energy he got from eating the chocolate muffin and is just running on the residual “fumes”.