Gillian Butcher From United Kingdom

Negative Temperature Is Hotter Than Hot

“Negative temperature is hotter than hot”,
The lecturer said to me.
Says I, quite bewildered, “It’s hotter than what?”
“Than positive infinity”.
“Oh my!” says I “what a perplexing thought.
Could you say that over again?”
“Negative temperature is hotter than hot”
perhaps I’d better explain:

The 1st law of thermodynamics”, he said
“is where I think we’ll begin.
And a population we’ll turn on its head
Caused by sluggardly spin.
So, from the 1st law, if we can win
A change in entropy
That’s negative with an increase in
Internal energy,
We will have a negative T,
Which is what we’re trying to find.
Now do you understand?” said he.

“But only in my mind.
For while in theory I agree
There’s negative Kelvin T
I can’t accept and cannot see
A negative entropy.
For everyone knows it’ll always increase
Till the world comes to an end.
And now you want it to decrease.
Nature’s laws you’re trying to bend.”

“It’s all to do with nuclei spin
and the time it takes to achieve
the spin/lattice equilibrium.
About 2 minutes, I believe.
If you apply a magnetic field
The magnetic dipoles will go
In the same direction, which will yield
An energy that’s low.
And now reverse the field so fast
To give yourself some time
For It’s a state that will not last
While the dipoles realign.
But while they’re in this disordered state
Due to this reversion
Now the energy’s high. We did just create
A population inversion.
Thus we have negative entropy
With increasing energy.
Thus we have negative Kelvin T.
It’s as I said it would be.”

So negative temperature is hotter than hot.
It’s really quite easy to see.
It’s hotter than — oh! What a wonderful thought —
Positive infinity.