Negative Temperature

Sorry I haven't posted much this week. I've been really busy in and outside of the lab. Negative temperature is something I encountered in my Statistical Mechanics course, but I didn't really understand it until I stumbled upon the wikipedia article on it.

First off, we're dealing with the Kelvin scale. There's nothing special about negative Farenheit or Celsius. Celsius is based off the freezing point of water and Farenheit is based off of... something? The important part is that the Kelvin temperature scale has it's zero as absolute zero. Absolute zero is a theoretical "cold limit" in that no physical system can actually reach this limit. Scientists have gotten to very low temperatures (.004 K is fairly common in condensed matter physics) but none have achieved absolute zero. So, with this in mind, when I say "negative kelvin temperature" you should be thinking something like "Wha...?"

Another aside: Negative temperature is actually a consequence of the definition of temperature and can only occur under a set of certain circumstances. No macroscopic system would ever be able to obtain such a state.

First let's look at the definition of temperature. Temperature is defined as the relationship between the change in energy of a system and the corresponding change in entropy. In calculus speak, T = dq/dS.

The system that we're going to consider is a nuclear spin system, that is a system of nucleons where we are only considering the energy associated with their spins. One caveat of negative temperature is that there must be a finite number of states in the system. For a spin system, that limit is two. A nucleon can either be spin up, or spin down. Nothing else. Also, we are assuming that the spin system is isolated from other sources of energy contribution (i.e., other degrees of freedom like vibrations, rotations, etc). We can make this assumption because the time scale at which this spin system receives energy from these other degrees of freedom is very large compared to the time scale in which we are considering this system. It's like assuming a radioactive element with a half life of 4 billion years won't decay during your experiment that will take 4 hours. Technically, it could decay since the probability for it to decay at each second is equal... but the probability is so low that you can safely ignore it. Now, moving forward...

Now let's say we apply a magnetic field to the system. What this does is break the degeneracy of the system. Before the magnetic field is applied both states of spin-up and spin-down have the same energy. With the magnetic field, those spins that align parallel to the field have a higher energy than the ones that align anti-parallel. Now, the second law of thermodynamics says that a system will evolve over time such that entropy is maximized (order to disorder). How this manifests itself in this system is an even distribution of spin-ups and spin-downs... a 50/50 split.

This is where the magic happens. There are certain techniques that allow you to flip the spin of the nucleons (say, from down to up) by using radio waves. By using these radio waves to move away from the 50/50 split, we are DECREASING the entropy of the system (since the maximum point of entropy is at 50/50) by ADDING energy, thereby creating negative temperature!

An interesting consequence of this is that negative temperature is hotter than positive! Heat will flow from a source of negative temperature to a source of positive temperature. So, the temperature scale goes (from cold to hot) like: 0 to +infinity to -infinity.

Work at the lab is going good. I've probably said this a billion times, but I think we're finally ready to wrap up the gas delivery system. I'll be glad to move on to something else :)