Negative-calorie foods
The claim, as heard: "Celery, cucumber, grapefruit — you burn more calories digesting them than they contain."
What the data show. Digesting and absorbing food does cost energy; it is called the thermic effect of food and it is a real, measured part of daily expenditure. It is also, by definition, a fraction of the energy in the food: around ten percent of intake on a mixed diet, higher for protein (twenty to thirty percent of the protein's energy), lower for fat and carbohydrate. No food has a thermic effect above one hundred percent of its own energy, because the measurement is of the energy spent processing what was absorbed. Celery is close to zero calories either way — a stick has a handful — and eating it costs about a tenth of that handful. The net is small and positive, not negative.
Verdict: false. Evidence grade A, because this is a matter of definition and of decades of measurement, not a contested finding.
The grain of truth. Very low-energy, high-water, high-fibre vegetables are excellent for a deficit — they fill the plate and the stomach for almost nothing — and protein's higher thermic effect is one small, real reason higher-protein diets help. Both are true without any food being "negative".
One sentence to remember: digestion costs a share of what you ate, never more than it; vegetables help because they are nearly free, not because they are below zero.
The daily energy step has the thermic effect in its place among the layers of expenditure.