
Negative temperatures are not colder than absolute zero - aatish
http://www.empiricalzeal.com/2013/01/05/what-the-dalai-lama-can-teach-us-about-temperatures-below-absolute-zero/
======
aatish
Hi. I'm the author of the post. I realize that it's a somewhat challenging
read, at least compared to my usual style, but my goal was to stay as true to
the physics as possible. I was a little disappointed with some of the popular
science coverage, because some sources made it seem like this is the first
time that physicists reached negative temperatures (not true), or that
negative temperatures aren't physical (they are, but they're weird!). I hope
you find it interesting.

~~~
ChuckMcM
That is a great exposition, it gets a bit bogged down in the money/happiness
analogy at times, but overall I felt like I understood what you were saying.
To test that, let me echo back what I think you said.

Physicists decided to define the temperature of a system not simply by the
amount of energy in the system, rather to define it as the ratio of the energy
in the system to the total entropy of that system. In so doing, they created a
situation where systems that go to a lower entropy state when energy is added,
are described as having a negative temperature.

~~~
jgeralnik
Small correction, not the ration of the energy to the entropy but the derivate
of the energy by the entropy - that is, the rate at which the energy increases
as the entropy increases.

(Of course, it's slightly more confusing since it's actually the inverse of
the temperature that's defined as dS/dE, which is the rate at which the
entropy increases as the energy increases, a much more understandable
definition. And as the physics professor who taught this to a room of students
from various departments said of the transition from

    
    
      1/T = dS/dE
    

to

    
    
      T = dE/dS
    

"The mathematicians in the crowd will be in an uproar now. But we can do stuff
like that in physics")

~~~
rfurmani
It's fine mathematics too, it's just like the chain rule (or interpreting the
d notation via infinitesimals/limits)

~~~
jgeralnik
The problem is in the assumption that the inverse derivative exists, which is
true for most functions in the real world but not for all (non-smooth)
mathematical functions.

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kqr2
If you understand entropy (which can be thought of as a measure of disorder or
randomness), then I think the Wikipedia definition is pretty clear.

    
    
      Systems with positive temperature increase in entropy as 
      one adds energy to the system. Systems with negative 
      temperature decrease in entropy as one adds energy to the 
      system.
    

<http://en.wikipedia.org/wiki/Negative_temperature>

<http://en.wikipedia.org/wiki/Entropy>

~~~
dchichkov
You can't add a single bit of information to a system with negative
temperature, - right or not?

~~~
jpdoctor
Not, and moreover, you've mixed apples and oranges.

A system's entropy in statisical mechanics is k log W, where k is Boltzmann's
constant and W is the number of microstates. The microstate is a configuration
of, say, electrons in energy levels.

Information theory has a quantity that behaves much like entropy in stat mech,
but is not actually entropy in stat mech.

BTW: The statement in stat mech would be - Adding energy to a system with
negative temperature reduces the number of microstates.

~~~
dchichkov
>> Information theory has a quantity that behaves much like entropy in stat
mech, but is not actually entropy in stat mech.

I was under the impression that these are exactly the same, rather than
analogous - <http://en.wikipedia.org/wiki/Landauer%27s_principle> ,
[http://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_i...](http://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_information_theory)
and so on (including recent advances).

And when I'm talking about adding a bit of information to the system - that's
similar to
[http://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_i...](http://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_information_theory#Szilard.27s_engine)

>>> Let's try more specific question. Laundauer's principle requires kT ln 2
of heat for every 1 bit of randomness erased from the system. What about
systems with negative T? I can't erase bits?

~~~
jpdoctor
The definitions in the second link are worth thinking about:
[http://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_i...](http://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_information_theory)

There is no requirement that information has a physical representation for
information-theoretic entropy. Landauer's result assumes that it does have a
physical representation, and derives some physical consequences.

~~~
dchichkov
Yes. You are right of course. There is no requirement that information
necessarily has a physical representation.

But, if I'm not wrong, this requirement could always be satisfied, for any
system with two or more microstates.

~~~
jpdoctor
A simple example where information-theoretic entropy is used where there is no
physical representation: Video codecs.

I'm guessing you've heard of mpeg and h.264 encoding. Which one encodes a
movie better? One way of answering this question is to ask: Which codec added
less entropy (perhaps for the same compression)?

For that matter: Before Shannon's information entropy, one might wonder if
there is a way (another codec) perhaps recovering the information after mpeg
coding and decoding. However, now you know that information-entropy can only
increase or stay the same, which tells you that subsequent "correction codec"
cannot remove entropy introduced by mpeg codec.

~~~
dchichkov
Thanks. I don't really like that example with codecs, because I could always
argue that any codec can only be a physical system, operating in some
environment at temperature T and will be constrained by Landauer's, ets.

Either way, I think we've digressed. I'm actually very happy with yours:
"Adding energy to a system with negative temperature reduces the number of
microstates.", because this is clear and unambiguous.

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lelf
"The temperature scale from cold to hot runs:

    
    
      +0 K, … , +300 K, … , +∞ K, −∞ K, … , −300 K, … , −0 K."
    

<http://en.wikipedia.org/wiki/Negative_temperature>

1/T makes more sense

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nilaykumar
Thank you for cutting through all the "science journalism" or whatever
bullshit, and actually bothering to put the _science_ in context (with some
humor too!).

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na85
99% of the time the silly analogies people try to make are more
misleading/confusing to the average person than the actual science.

This is one of the 99%

~~~
Xcelerate
Haha, right there with you!

"The Higgs boson is like pearls moving through molasses" or "a celebrity
moving through a bar".

"Spacetime is like a big sheet of fabric with a bowling ball on it."

Yeah... no.

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NanoWar
I love the analogies! "What happens when a negative temperature object meets a
positive temperature object? To find out, imagine that the Dalai Lama meets
Warren Buffett." Very interesting.

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GIFtheory
Too complicated. IANAP, but it sounds like they just created a gas in which
particles are more likely to be found at higher (absolute) temperatures than
lower temperatures, which is the opposite of what usually happens
(<http://en.wikipedia.org/wiki/Boltzmann_distribution>). In fact, from the
abstract of the paper itself:

"Absolute temperature is usually bound to be positive. Under special
conditions, however, negative temperatures—in which high-energy states are
more occupied than low-energy states—are also possible..."

~~~
Dylan16807
But "more particles are high-energy than low-energy" is pretty meaningless. It
doesn't explain at all why a system so close to absolute zero would give away
energy to boiling water, for example.

~~~
yk
The answer is perhaps somewhat technical, but hopefully this shows the
argument why heat flows from negative to positive temperature.

Entropy is essentially the (logarithm of) the number of states a system can be
in, without changing the macroscopic observables. These states have all the
same probability. The second law of thermodynamics is then simply a
consequence of the number of allowed transitions of the system. And
temperature is the change of the number of states if energy is added to the
system. That heat flows from the lower (positive) energy to the higher is then
a consequence of calculating the probabilities, as is the observation that
heat flows always from a negative to a positive temperature system.

Perhaps a example will make this somewhat clearer: Think of a chain of 20
capacitors, each can be charged or uncharged and I call the 10 left capacitors
my left subsystem, and the 10 on the right the right subsystem. Initially
there is 1 charged capacitor in the left and 3 in the right. Then the
probability that after one charge moves there are two charged capacitors in
each subsystem is 9/16 ( since 9 of the uncharged capacitors are on the left).
In this case the temperature is positive in both subsystems. (The number of
possible configurations of the left 10 capacitors is higher for two charged
ones ( 5*4) than for one charged ( 5).

The negative temperature case would in this analogy be, if in one subsystem
there are more than 5 charged capacitors. Then there are more charged than
uncharged capacitors, the number of allowed states would decrease if I add
additional charge. ( I can distribute 9 charges in 10 different ways, but 10
charges just in one way.) But nothing happens about the argument of transition
probabilities. If there are 7 charged capacitors on the left and 2 on the
right, then after moving a charge the probability that there are 6 and 3
charged ones is 8/11 ( 8 of the 11 uncharged capacitors are on the right).

In the case of the boiling water and the negative (close to zero) system it is
the same, it is about counting possible states. And since in one the number of
states increases if I add energy ( the temperature is positive) and in the
other the number of states increases if I remove energy ( the temperature is
negative), both have a preference for transferring energy from the negative
energy system to the positive one.

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tsahyt
I've been coding too much. Once I read that that objects with negative
temperature behave as if they were hotter than objects that are at any
positive temperature, my first thought was along the lines of "well yes,
overflow". I should get out more.

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arasmussen
"In fact, as I’ll try to explain, objects at a negative temperature actually
behave as if they’re HOTTER than objects that are at any positive
temperature."

So... overflow? :)

~~~
pavel_lishin
It's all a simulation!

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drucken
Interesting intersection of utility functions in finance and physics!

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Tycho
Wait, how is a rich Buffet giving money to a poor Buffet a net increase in
energy? Isn't this a zero sum system?

~~~
pavel_lishin
Not energy, but entropy.

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TheAmazingIdiot
The energy curve sounds like a parabola (f(x)=x^2) curve of "energy", where
nothing can actually sit at 0,0 or go through it.

The energy translation used to flip a slight positive temp to a negative temp
sounds like a reflection to the negative side of the curve.

~~~
yaks_hairbrush
Another way to look at it is that the important quantity is not temperature,
but its reciprocal. Absolute zero becomes infinity under this transformation,
hence unattainable. Heat energy will flow from lower 1/T to higher 1/T, and
more heat energy added to a system lowers the 1/T quantity of that system.

