Why is it faster to reheat something than it is to cook it?

"Cooking" is often a chemical process. Denaturing proteins, gelatinization, causing chemical reactions like browning, or even causing state changes like evaporation.

In many cases for these reactions to happen, we need to overheat the food. (Cook it and let it rest to cool off back down to undo some of the changes that were made and/or bring it back down to a reasonable temperature to eat). This is true when grilling meats, frying, baking bread, and lots of other types of cooking.

Other times, we need to bring something to temperature and hold it there for some period of time. This holds for extracting collagen, starch gelatinization (eg, cooking pasta, potatoes, etc.) but also just waiting for flavors to transfer in soups and similar dishes.

With warming, you're just adding enough heat to it to move it a few degrees, but you're not typically trying to change the state of the food, so less total energy is needed.

Now, it is always faster to reheat vs. cook things? For the most part it's true, but I suspect that there would be an edge case out there. Something that's cooked from room temperature, but then stored chilled and the chilling causes issues (like retrogradation in starches, maybe?) that make them more resist than reheating.

This is because when you're cooking some foods you're not just heating it up. A lot of foods are boiled, not because they need to be heated up, but because they need to absorb water. We just boil the water because that makes the hydration go a lot faster (the high temperature is also needed to break down some of the starches, for more info, see here).

With soup it should take about the same time, if you don't care about dissolving/softening the vegetables into the soup. That also takes time, with vegetables the chemical reaction involved is mainly breaking down the pectin that holds the cells of the vegetable together.

With meat, dissolving/denaturing the collagen (stuff that holds everything together) into gelatin also takes time. Also you want a different temperature for reheating than frying because with meat you want a nice crispy brown outside (Maillard reactions), and for that you need far higher temperatures than the inside of your meat.

It doesn't even seem to matter on the method of reheating, as I can reheat something faster if I use the same method of as I did to cook it (e.g. by frying).

Note that I always check the temperature of something I've reheated via a food-probe, so I'm also not making a mistaking of cooking something to 70C and then reheating to 45C etc.

That is not strictly possible. If you are imparting the same amount of heat energy to the same thing at the same rate in the same controlled environment, then the resulting temperature must necessarily be identical.

If you are ensuring a consistent overall temperature resulting from the same source, then the time difference arises because you are heating different things.

One likely culprit would be water that escaped as steam during during cooking or evaporated during/after, which reduces the mass you are heating the second time around. Water is also one of the slowest things to heat, because it has one of the highest specific heat capacities amongst common substances. This alone would result in a very noticeable difference in many types of food.

Because heating up is merely rising the temperature of a body and how much its temperature change depends on its specific heat. The sane is for the complex mix of the various items in the pot as we are speaking about kitchen.

Cooking involves a number of physical and chemica processes, each of which takes time. Is this taking time the major difference, that is why I've decided to add this answer alongside the others. They aren't wrong at all, just in a way incomplete. Cooking must be accomplished, and that will be the case anyway, see just here below.

Most of these process require heat as well, that is energy must be given to the system. So the pot must stay on stove (or the meat on the grill, etc.) longer.

Independent of this energy requirement, which for some chemical transformations can be even positive (ie the process releases energy and not vise versa), chemical reactions go faster higher the temperature is. For instance, pasta could be cooked at lower than boiling point, just it will take longer. This is why pressure cooking is somehow faster as well less energy consuming.

edited.

Specifically to question number 1, yes is at least in principle possible that a cooked item takes longer to be heat as compared to heat the original item. If cooking involved water intake, the specific heat of the cooked item might be bigger, for instance. An example is likely pasta. I would expect that it takes longer to bring a cooked spaghetto to 100 °C than doing it with a raw one. But this analysis is certainly out of the kitchen (fine measuring, ad hoc experiments, way of heating....), as probably we never put raw vs cooked spaghetti on a hot plate and measure how long it takes for them to reach the wanted T.

Does this question really call for a scientific explaination ?

To cook, you heat something and let it stay hot until it get cooked. To heat, you just heat it a bit until you can eat it.

So even it you want to eat it as hot as its cooking temperature (which you won't in most cases, with a good 100°C margin), you just ignore all the "cooking time" after you reached the right temperature.