Time&Temperature vs energy needed for molecules structure's changes

The hypothesis is somewhat valid. The version which is true is: there is a correlation between the total amount of energy which went into the meat and the degree of doneness. And because the total energy is the rate of energy input multiplied by the time you are adding energy to the system, time and heat are interchangeable to some extent.

However, there is no constant "total amount of energy" which needs to go into the meat. Protein denaturing is a complicated stochastic process. If we were to assume that we have a uniform thin layer of meat and a perfectly uniform heat source parallel to it, we still wouldn't have a constant total amount of energy. It is a bit less noticeable with meat, where preparation methods are limited (*), but in eggs it is easy to observe that the speed at which yolks are heated will have a noticeable difference on the final texture of a custard.

Even if you could get away with a usable range for the "total amount of energy", you could still not predict the time needed by a given piece of meat at a given temperature. We are talking about a complex nonlinear system here. That part is a duplicate of another question, so I will simply post a link to my older answer.

So in the end, there is a very good reason why you should check for doneness instead of try to predict doneness. Or, in the special case of sous vide, use the empirically determined charts somebody else went to all the trouble compiling. Calculating it for yourself is completely impractical.

There are two big things going on when you cook meat:

• bringing it up to the desired temperature
• holding it there long enough for desired changes to occur

For some meat, the temperature is basically all that matters. The most common example of this is a steak: once it's the temperature you want, it's done. You might finish it off by searing it to cook the outside a bit extra, but the doneness of the bulk of the meat depends purely on the temperature.

For other kind of meat, the temperature is just the first step, and the cooking you really want happens as you hold it there. Anything with a really long cooking time is likely in this category, like the 24-48 hour pork cheek you mentioned, or perhaps more commonly, slow-cooked pork shoulder or ribs. That long cooking lets the connective tissue break down (notably collagen turning to gelatin), taking it from chewy and tough to pull-apart tender. It'll break down at temperatures as low as 50C/120F, but as you increase the temperature it'll break down faster and faster, up to 80C/180F.

Some of those reactions might be endothermic, but protein hydrolysis is actually slightly exothermic. The energy is also way, way smaller than the energy you use to heat the meat - for cooking purposes, you can ignore it. In any case, trying to model heat transfer and heat input is kind of pointless: it's the reaction rate that matters, not the energy you're using/wasting to keep it at that temperature. The reaction rate does increase with temperature, as mentioned above, but again that's about temperature, not energy input.

So how does that all connect to your energy hypothesis?

Bringing meat up to the desired temperature is basically all about energy: you have to transfer a fixed amount of heat energy to bring a given amount of meat to a given temperature. So in that sense, you're spot-on.

But when you're holding meat at a temperature to cook it, you're not transferring significant heat into it anymore. It's really just about time. The amount of time it takes does often depend on the temperature, since the reaction rates are temperature-dependent, and that's why you've see the variation in time and temperature in recipes. But it's no longer a simple matter of energy input as you guessed. Yes, you'll have an initial period of bringing the meat up to temperature, which is simple heat transfer, but the real cooking happens after that.

Heat transfer is going to be the temperature difference X area X coefficient X time.

Since the temp of meat changes it would really be an integral equation but let's not make it hard.

There is also obviously a minimum temp as meat does not cook in a refrigerator. The guideline from USDA is cook pork to 145 F / 63 C so that would be the minimum cooking temperature and it would take a while. That 65 is very close to the finish temp.

What meat temp would have those two heat transfer the same

48(65-t) X a X c = 24(80 - t) X a X c
2(65 - t) = 80 - t
130 = 80 + t 50 C = t = 122 F
But that is taking a constant temp so finish temp would be higher

If you extrapolate this to 36 hours you are going to be pretty much at final meat temperature.

The meat has an initial and final state. It takes fixed amount of heat to break it down. Temperature is not what cooks the meat. Heat cooks the meat and temperature is what drives the heat transfer. It is done when it gets to a final temperature but heat transfer is what got is there. The cooking temperature needs to be at least final meat temperature or heat transfer stops.

You would need to take case by case. You are only going to get estimates with heat transfer equations.