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By its simplest definition, a calorie is a unit of energy. More scientifically, each calorie is the amount of energy needed to raise 1 gram of water by 1 degree Celsius.
Calories come from three main macro nutrients: protein, carbohydrates, and fats.

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Just like how a dog is a dog,  or a desk is a desk, a calorie is a calorie. All calories have the same amount of energy, that being 4,184 joules of energy. The first law of thermodynamics states that the energy of an isolated system is constant. For example, in a laboratory setting, if 1,000 calories of broccoli and 1,000 calories of soda were burned, the same amount of energy would be released.

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<- Whilst those statements are technically true, there are many different kinds of dogs or desks, and same goes for calories. Also the law of thermodynamics cannot be applied to living, breathing, digesting systems. The human body is a highly complex biochemical system with elaborate processes that regulate energy balance.

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Different foods go through different metabolic pathways, some being more efficient than others (more of the food's energy is used for work and less is dissipated as heat). The thermic effect is a measure of how much foods increase energy expenditure, due to the energy required to digest, absorb and metabolize the nutrients.
The thermic effect of the different macro nutrients:
Fat: 2-3%
Carbs: 6-8%
Protein: 25-30%
Going with the thermic effect of 25% for protein and 6% for carbs, this would mean 100 calories of protein would end up as 75 calories, whilst 100 calories of carbs would end up as 94 calories.
Therefore, calories from protein are less fattening as they take more energy to metabolize.

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Certain foods fill us up more than others without being full of calories (such as vegetables), whereas others loaded with calories don't make us feel satiated at all (i.e soda, chips, candy). This means you may be likely to overeat on some foods more than others. For example, it'd be a lot easier to consume 500 calories of ice cream, while you'd have to be force fed 500 calories of broccoli. The satiety index is a measure of the ability of foods to reduce hunger, increase feelings of fullness and reduce calorie intake for the next few hours. If you eat foods low on the satiety index, then you will be hungry and end up eating more and vice versa.

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These are the two main simple sugars in our diets and gram for gram, the two provide the same number of calories. However the way that they are metabolized in the body is completely different. Glucose is able to be metabolized by all of your body's tissues, but fructose can only be metabolized by the liver in any significant amount. Consuming a lot of fructose can cause insulin resistance, abdominal fat gain, or increased blood sugar (added sugar and candy being its largest dietary sources). Also, fructose does not stimulate the satiety centers in your brain in the same way as glucose, leading to a reduced feeling of fullness.
Even though fructose and glucose provide the same number of calories, fructose has far more negative effects on hormones, appetite and metabolic health.
NOTE: Whilst fruits contain fructose, they're also rich in fiber and water, which ends up mitigating the negative effects of fructose.

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Do Calories Matter? Is a Calorie a Calorie? (Science of Weight Gain)

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It is a drastic oversimplification to say that "a calorie is a calorie" or "all calories are created equal". Different calorie sources can have vastly different effects on hunger, hormones, energy expenditure and the brain regions that control food intake.

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https://shapescale.com/blog/health/nutrition/why-macronutrients-are-important/

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This is a measure of how quickly foods raise blood sugar. Refined carbohydrates such as white bread or rice and added sugars have a high glycemic index, as they tend to be low in fiber and are digested and absorbed quickly, leading to rapid spikes in blood sugar. This tends to lead to a crash in blood sugar a few hours later. When that happens, you crave for yet another high-carb snack, leading to over-eating. A study found that teenage boys ate 81% more calories during a high-GI compared to a low-GI meal!

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... We all intuitively know that equal caloric amounts of soda and broccoli can’t be the same nutritionally. But as Mark Twain said, “The problem with common sense is that it is not too common.”

Dr. Mark Hyman, family physician, director of the Cleveland Clinic Center for Functional Medicine, chairman of the board of the Institute for Functional Medicine

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1. Healthline, Gunnars K, 08/05/2018: <https://www.healthline.com/nutrition/6-reasons-why-a-calorie-is-not-a-calorie>
2. Mark's Daily Apple, Sisson M, 08/01/2019:<https://www.marksdailyapple.com/are-all-calories-the-same/>
3. Nerd Fitness, "Steve", unknown date:<https://www.nerdfitness.com/blog/is-a-calorie-really-just-a-calorie/>
4. Intensive Dietary Management, Dr. Fung J, unknown date:<https://idmprogram.com/a-calorie-is-a-calorie-part-ii/>
5. Children's Hospital, Boston, Division of Endocrinology, Ludwig DS, Majzoub JA, Al-Zahrani A, Dallal GE, Blanco I, Robert SB, 03/1999: <https://www.ncbi.nlm.nih.gov/pubmed/10049982>
6. Dr. Hyman, Hyman Mark MD, unknown date: <https://drhyman.com/blog/2014/04/10/calories-dont-matter/>

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https://www.physioanswers.com/2016/09/calorie-density-how-to-lose-weight.html