# Negative absolute temperatures

I read that scientists created a substance that was below absolute zero. How is that possible? Is it some mathematical quirk in how they calculate temperature, or can it actually be said to be physically ‘colder’ than something at absolute zero? What are alternate definitions of temperature

In: Physics

Share

Impossible. Not only is it also only theoretically possible for the temperature to reach -273°C (0K), no matter how much more heat you drain, you cannot get the temperature to drop further

I believe you’ve got a great answer from /u/r3dl3g but I just couldn’t leave this thread without attempting to explain entropy a bit more as he gave the thermodynamic view, the statistical physics one is the one for me…

So let’s say you’ve got some physical system (a glass of water for instance), in the micro scale this system is made of constituents, the water is basically a huge collection of water molecules right? now there are many ways to arrange those molecules and still in the macro scale, we would see the same glass of water, many microscopic arrangements lead to the same macroscopic one.

Entropy is just saying, if this water glass has this much energy, how many arrangements could possibly result in it? (for those interested Entropy = Kb * natural log (number of arrangements at given energy) where Kb is just some constant).

Now we can define temperature 1/T = dS/dU basically the temperature is the answer to the question “hey, if we where to add a bit of energy to this glass of water, how does the number of arrangements change?” normally we would expect the number of arrangements to increase, I mean the water molecules would be swooshing around faster and in more ways, makes intuitive sense at least right? increasing number of arrangements would mean positive temperature according to the definition, but who’s to say that they can’t decrease? that would mean negative temperature…

now going back to /u/r3dl3g’s answer, what he means in that negative temperatures are hotter is that the ordering of events goes : We add energy -> Entropy increases -> We add more energy -> Entropy increases even more -> We add more energy -> Ah, guys? I think we overdid it -> Entropy decreases as the current setup is unstable. To reach negative temperatures you must first pass through positive temperatures.

Beyond the physics here, be aware that scientists like to play games with definitions and categories. A lot.

They break the speed of light, reverse time, create negative energy, raise the dead and do all kinds of other “impossible” things all the time…using technical loopholes and novel definitions that don’t actually break the laws of physics. In fact, they often don’t even claim to do any of these things, it is often a headline written by a ignorant editor for a story written by a science illiterate journalist based on information provided by a slimy university PR flak.

Temperature is definitionally a measure of thermal energy in a system, such that when thermal energy increases in the system, temperature likewise increases.

Typically, when we impart some form of energy (not necessarily thermal) from an outside source to the system, part of that energy is converted to thermal energy in the system and so we get a nice rule of thumb that imparting energy to a system increases is temperature. Or, since temperature can only be measured from 0K and above, we can say that imparting energy to the system moves it further from absolute zero.

It is possible to artificially create a system that behaves in an opposite manner to the above description. If we were to impart energy to such a system, it would actually lose thermal energy, or in other words, it’s temperature would approach absolute zero. Because this behavior is what would be expected of a system if it were possible to have negative temperature, it is sometimes called by that name.

>Is it some mathematical quirk in how they calculate temperature, or can it actually be said to be physically ‘colder’ than something at absolute zero?

It is *kind of* a mathematical quirk, although it has a real physical meaning, but also isn’t actually “colder” than. You could argue that -0 K is the “hottest” possible temperature.

The tl;dr of all of this is temperature, as a quantity, is fucking *weird*, and our entire ingrained concept of what temperature is may arguably be a mathematical hindrance.

To start, the definition of temperature that everyone has ingrained into them (i.e. temperature is proportional to the vibrational/rotational/kinetic energy of the atoms and molecules of a substance) is incorrect(ish). It’s a very useful way of thinking about temperature from a layman’s perspective, and is functionally a good way to actually measure temperature for the overwhelming majority of situations, but it’s actually not correct.

Thermodynamically, temperature actually has a precise definition, and is directly tied to the relative rates of change of energy and entropy of a substance (if you know calculus, the definition is that T = dU/dS). Without diving into what entropy is (as that’s another abyss of weird); for most normal everyday temperature ranges, energy and entropy are basically in lockstep; as one increases, so does the other. However, as you get hotter and hotter, you get into diminishing returns; the rate of increase of entropy slows down. Eventually it inverts, such that as you pour more energy into a substance, the entropy of that substance *decreases*, and as a result you’re in the negative temperature range. Thus, the temperature scale, from coldest to hottest (for lack of a better word), is;

0 < 300 < inf < -inf < -300 < -0

This makes the math more than a little wonky, which is tied to the fact that we actually seem to have been using temperature semi-incorrectly in physics (although for most problems it’s a non-issue, as the universe doesn’t seem to tolerate negative absolute temperatures for long time periods on a macro-scale). As a result, in many statistical thermodynamic settings, temperature is actually replaced with what’s called Thermodynamic Beta, which is;

β = 1/(T*kb)

where kb is the Boltzmann constant. This “fixes” the temperature scale from a mathematics perspective, as now temperature is used to measure *coldness*, and the same scale as above now goes from;

inf < M < 0 < -0 < -M < -inf

where M is just some finite temperature corresponding with 300 K (i.e. room temperature) from the above scale, just for completeness’ sake.