It's found it's way into the "minimal valley" whereas an arbitrary lukewarm state might be closer to a "ridge".
Clearly, yes, if you could start at the magic state that would be ideal. And there should be experiments that use a bunch of thermometers too compare the time from the same average temp (the initially warmer one just gets the "running start").
Mathematically it is not hard to abstractly characterize what is going on. (This is not saying the actual physics is easy!!) Temperature is an equivalence class on fluid states, but the average time to transition between those states does not form a metric space. The failure of the triangle property shows that the composition of transitions induces non-uniform distributions within the temperature equivalence classes that subvert the expected transition time by which we had attempted to build a metric space to begin with.
Just like non-euclidian space in the 19th century, this is the sort of thing where the mathematics can say "yeah sure seems legit" before the physics stops saying "wait wtaf",
1. Temperature is monotonically related to energy content. A warmer system has more energy than a colder one, all else being equal.
2. To cool, a system must release energy. The rate at which a system can release energy is monotonically related to the difference in temperature between the cooling system and the cold sink to which its energy is being released. The bigger the temperature difference, the higher the rate of energy release (all else being equal).
For the Mbemba effect to be real, one of those two premises must be false. Which one is wrong?
> Temperature is monotonically related to energy content. A warmer system has more energy than a colder one, all else being equal.
In equilibrium, the temperature of the water is directly related to the energy content, with the heat capacity being the conversion factor.
But under the thermodynamic definition, the temperature of the system depends not only on its energy but also on its entropy. And one of the points the article is making is that even when we know the total amount of energy entering or leaving the system, its entropy may not be nearly so easy to measure or calculate when its state is far from equilibrium.
Sorry, but that is not true. The definition of the SI unit of temperature, the Kelvin, is given in terms of Boltzmann's constant, which has units of Joules (i.e. energy) per Kelvin.
I don't think either one is false. To me, 2 looks false if you consider the "system" in question to be the entire glass of water. But my interpretation is that in this case the glass of water is really many very small systems (pockets of unequal amounts of energy) all interacting with each other.
Let's say you're given a few hot potatoes and have to cool them down as fast as possible. You have a refrigerator but you can only keep one of them in it at a time. How do you decide which one to put in at any given time so they all reach temp the fastest? When the "system" involves many possible pairings of temperature differentials it feels very intuitive that some configurations would be better than others. So it removes the mind-bending thermodynamics law breaking aspect of it.
Admittedly, this isn't really what the article says! I honestly don't get how my above intuition squares with the whole energy minima thing, and so while useful as a thought exercise to at least help me entertain the idea, I'm not really sure it's correct?
IIRC (my thermodynamics is a long time ago), but 2 applies only when the two (cooling system and sink) are near equilibrium, which is not the case here.
That would imply that water once heated and then cooled is different from water never heated - at least for a time. I wonder if there is any evidence for that.
One difference could be that hot water is not as good a solvent for gas (think soda bubbles). So heated water would have shed most of its gas content which would lead to a different (faster?) freezing process, if freezing occurs faster than gas can dissolve back in.
It's found it's way into the "minimal valley" whereas an arbitrary lukewarm state might be closer to a "ridge".
Clearly, yes, if you could start at the magic state that would be ideal. And there should be experiments that use a bunch of thermometers too compare the time from the same average temp (the initially warmer one just gets the "running start").
Mathematically it is not hard to abstractly characterize what is going on. (This is not saying the actual physics is easy!!) Temperature is an equivalence class on fluid states, but the average time to transition between those states does not form a metric space. The failure of the triangle property shows that the composition of transitions induces non-uniform distributions within the temperature equivalence classes that subvert the expected transition time by which we had attempted to build a metric space to begin with.
Just like non-euclidian space in the 19th century, this is the sort of thing where the mathematics can say "yeah sure seems legit" before the physics stops saying "wait wtaf",