# Eli5: Negative tempretures (on the Kelvin scale)

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I don’t understand how atoms that are in the “negative tempretures” have 0 entropy while being insanely hot. I also dont get how negative temperatures are hotter than infinity if (planck’s temperature forbids this; dont really know if it does). Please explain!

In: Physics

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Quantum thermodynamics isn’t macro physics as you interact with temperature in your kitchen. In macro physics, 0˚K is “absolute zero”, where there is no heat. You can’t get a block of metal to 0˚K, even in a lab, though you can get very close.

In exploring why you can’t get to 0˚K, scientists have determined that the macro physics of temperature isn’t right. Alas, this has happened before when they determined that the macro physics of motion isn’t right either. Macro physics is right enough for almost everything you do, like cook or drive a car, but it’s not right enough for everything.

Quantum physics of temperature, like quantum physics of mechanics, is quite counter-intuitive, it just seems wrong. However, quantum mechanics has been proven accurate in many scientific experiments. It is our best understanding of the world of the small, though there are still issues and 100 years from now some redditor may be making the same statement about it in favor of a proven string theory.

Quantum thermodynamics has a notion of negative temperature, and heat flows from an object with negative temperature to an object with positive temperature – the macro thermodynamics definition of “hot”. However, you can’t mix macro thermodynamics and quantum thermodynamics, that’s the whole point of quantum thermodynamics.

There’s two ways to define temperature:

* How much the molecules of a substance are moving, on average.
* How much the entropy, or difficulty-to-predict, of a substance is affected by adding energy.

The first is the day-to-day usage. Molecules moving is heat energy; the average amount of movement in a substance is that substance’s temperature.

The second usage is used by physicists. Most of the time, they’re the same; as you add heat to a substance, its molecules move more and become harder to predict, thus entropy increases. That’s a positive temperature. A negative temperature would be the opposite situation – adding energy reduces chaos, makes things easier to predict.

In some very strange and rare substances, adding heat can *reduce* the chaos in that substance. For instance, atoms spin; in certain circumstances, the direction the atoms are spinning will be random, fully chaotic, max entropy. But by adding energy to the system, we can actually making more and more of the atoms spin in the same direction. Thus, adding energy is decreasing entropy – which means that the temperature of the substance is negative.

It comes from the proper definition of temperature.

Usually we think that ading more energy to the thing makes it hotter. This is good enough for most situations.

But this is not how temperature actually works. When you add energy to a thing you will also increase entropy in the thing. The rigorous definition of temperature comes from the relation of how much the entropy increases when energy is added.

Well most of the time adding energy increases entropy. It is possible to build things that behave the opposite way. When you add energy to this thing the entropy in it decreases. According to the definition of temperature this is negative temperature on kelvin scale.
The way this works is that normally the particles can just go to higher energy states when you add energy. But in this system there is some ceiling. So when you add energy you will just put more atoms to their maximum state, more atoms at same state means less entropy. Also more atoms at maximum state means they really want to give that energy away so it heats up anything it touces and is “really hot”.

basically temperature is the direction in which entropy rises (with energy). For macroscopic systems, the number of possible states (the entropy) usually rises (very strong) with energy. Hence temperature is positive. if you have two macroscopic systems they will exchange energy such that their combined entropy will be maximized. That means some tiny bit of energy lost here will reduce the entropy precisely as much as it will rise the entropy there. Hence they will equalize in temperature.

For quantum systems, the number of states can reduce with energy. (take semiconductors near their bandgap). In this scenario the temperature is negative: as you increase the energy less states become available. Since two systems will still try to find maximum entropy, the negative temperature part will drain it’s energy and pump it into the positive temperature part until both (then positive) temperatures are equal.

The temperatures still equalize, but the energy flow is reversed (from the negative to the positive temperature parts, instead from the higher to the lower temperature parts). So in a way, regarding energy flow, negative temperature parts are hyper-hot, as they dump their energy into anything with positive temperature.