Absolute hot

There’s only one absolute zero but there are multiple absolute ‘hots’, depending on the temperature at which various theories of physics break down. This is an interesting conception because, while absolute zero is very well-defined and perfectly understood, absolute hot simply stands for the exact opposite not in a physical sense but in an epistemological one: it is the temperature at which the object of study resembles something not understood at all. According to the short Wikipedia article on it, there are two well-known absolute hots:

1. Planck temperature – when the force of gravity becomes as strong as the other fundamental forces, leading to a system describable only by theories of quantum gravity, which don’t exist yet
2. Hagedorn temperature – when the system’s energy becomes so large that instead of heating up further, it begins to produce hadrons (particles made up of quarks and gluons, like protons and neutrons) or turns into a quark-gluon plasma

Over drinks yesterday with the physicist known as The Soufflé, he provided the example of a black hole. Thermodynamics stipulates that there is an upper limit to the amount of energy that can be packed into a given volume of space-time. So if you keep heating this volume even after it has breached its energy threshold, then it will transform into a black hole (by the rules of general relativity). For this system, its absolute hot will have been reached, and from the epistemological point of view, we don’t know the microscopic structure of black holes. So there.

However, it seems not all physical systems behave this way, i.e. become something unrecognisable beyond their absolute hot temperature. Quantum thermodynamics describes such systems as having negative temperatures on the kelvin scale. You are probably thinking it is simply colder than absolute zero – a forbidden state in classical thermodynamics – but this is not it. There seems to be a paradox here but it is more a cognitive illusion. That is, the paradox comes undone when you acknowledge the difference between energy and entropy.

The energy of a system is the theoretically maximum capacity it has to perform work. The entropy of the system is the amount of energy that cannot be used to do work, also interpreted as a degree of disorderliness. When a ‘conventional’ system is heated, its energy and entropy both increase. In a system with negative temperature, heating increases its energy while bringing its entropy down. In other words, a system with negative temperature becomes more energetic as well as is able to dedicate a larger fraction of that energy towards work at highertemperatures.

Such a system is believed to exist only when it can access quantum phenomena. More fundamentally, such a system is possible only if the number of high energy states it has are limited. In classical systems, which is anything that you can observe in your daily life, such as a pot of tea, objects can be heated as high a temperature as needed. But in the quantum realm, akin to what classical thermodynamics says about the birth of black holes – that its energy density became so high that space-time wrapped around the system – systems of elementary particles are often allowed to have possess only certain energies. As a result, even if the system is heated beyond its absolute hot, its energy can’t change, or at least there will be nothing to show for it.

While it was a monumentally drab subject in college, thermodynamics – as I have learnt since – can be endlessly fascinating the same way, say, the study of financial instruments can illuminate the pulse of capitalism. This is because thermodynamics – as in the study of heat, energy and entropy – encapsulates the physical pulse of the natural universe. You simply need to go where its laws take you to piece together many things about reality.

Of course, a thermodynamic view of the world may not always be the most useful way to study it. At the same time, there will almost always be a way to translate some theory of the world into thermodynamic equivalents. In that sense, the laws and rules of thermodynamics allow its practitioners to speak a kind of universal language the way Douglas Adams’s Babel fish does.

The most famous example of this in the popular conception of scientific research is the work of Stephen Hawking. Together with Jacob Bekenstein and others, Hawking used thermodynamic calculations to show (on paper) that black holes were mortal and in fact emitted radiation out into the universe, instead of sucking everything in. He also found that the total entropy contained inside a black hole – its overall disorderliness – was closely related to its surface area. This was in the 1970s, but the idea that there are opportunities to understand the insides of a black hole by studying its outsides is as profound today as it was then.