Fast diet, why does it work for weight loss?

Why does intermittent fasting increase metabolism? And because the famous Fast diet (a pun that means both fast diet and fasting diet) also called the intermittent fasting diet or the 5: 2 diet continues to be one of the most followed diets after more than a year , while the Is the book by Dr. Mosley and the reporter Spencer who developed it still a bestseller?
If we were to strictly consider the calorie calculation, the Fast diet would make no sense: for two days a week you eat 500 calories if you are a woman and 600 if you are a man. The other days of the week you can eat normally, even if Dr. Mosley clarifies that in the days of no diet, no less than five, it is not the case to go crazy and eat everything , but to live them normally, perhaps eating genuinely, without lingering in refined foods and snacks.

However, even if we considered losing two thousand calories a week or three thousand with the Fast diet, we would usually lose less than half a kilo a week , eating normally even less the other days, because we must consider that in the days immediately following those of fasting we will tend to eat more than usual. In short, if we were to consider only the caloric discourse, the calories lost would be few even to be able to drop two kilos a month.
On the other hand, those who have followed the Fast diet have lost much more and the authors of the diet reply that the two non-consecutive days of fasting cause an increase in metabolism: therefore, in addition to cutting calories, the body burns more. Mosley goes so far as to say that even immune defenses, energy levels and so on increase. But all this is written in the book, ok, but what scientific basis does the Fast diet have?