7 ms·

Negative temperatures are not colder than absolute zero

266 points by aatish 14y ago

nilaykumar 14y ago
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!).
GIFtheory 14y ago
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 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 14y ago
  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 14y ago
    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.
  - mg74 14y ago
    I read through the article and the comments and felt I almost understood what was going on but was still missing something. Your example then made it all click for me in one of those "Aha!" moments. Thank you.
TheAmazingIdiot 14y ago
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 14y ago
  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.
NanoWar 14y ago
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.
aatish 14y ago
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 14y ago
  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 14y ago
    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 14y ago
      It's fine mathematics too, it's just like the chain rule (or interpreting the d notation via infinitesimals/limits)
tsahyt 14y ago
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.
lelf 14y ago
"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 http://en.wikipedia.org/wiki/Negative_temperature 1/T makes more sense
drucken 14y ago
Interesting intersection of utility functions in finance and physics!
na85 14y ago
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 14y ago
  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.
kqr2 14y ago
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/Negative_temperature http://en.wikipedia.org/wiki/Entropy http://en.wikipedia.org/wiki/Entropy
- dchichkov 14y ago
  You can't add a single bit of information to a system with negative temperature, - right or not?
  - deleted 14y ago
    [deleted]
  - jpdoctor 14y ago
    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 14y ago
      >> 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/Landauer%27s_principle , http://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_information_theory http://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_i... 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_information_theory#Szilard.27s_engine http://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_i... >>> 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?
arasmussen 14y ago
"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 14y ago
  It's all a simulation!
Tycho 14y ago
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 14y ago
  Not energy, but entropy.

266 points by aatish 14y ago

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!).

GIFtheory 14y ago

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 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 14y ago
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 14y ago
  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.
- mg74 14y ago
  I read through the article and the comments and felt I almost understood what was going on but was still missing something. Your example then made it all click for me in one of those "Aha!" moments. Thank you.

TheAmazingIdiot 14y ago

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 14y ago
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.

NanoWar 14y ago

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.

aatish 14y ago

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 14y ago
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 14y ago
  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 14y ago
    It's fine mathematics too, it's just like the chain rule (or interpreting the d notation via infinitesimals/limits)

tsahyt 14y ago

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.

lelf 14y ago

"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 http://en.wikipedia.org/wiki/Negative_temperature 1/T makes more sense

drucken 14y ago

Interesting intersection of utility functions in finance and physics!

na85 14y ago

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 14y ago
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.

kqr2 14y ago

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/Negative_temperature http://en.wikipedia.org/wiki/Entropy http://en.wikipedia.org/wiki/Entropy

dchichkov 14y ago
You can't add a single bit of information to a system with negative temperature, - right or not?
- deleted 14y ago
  [deleted]
- jpdoctor 14y ago
  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 14y ago
    >> 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/Landauer%27s_principle , http://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_information_theory http://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_i... 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_information_theory#Szilard.27s_engine http://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_i... >>> 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?

arasmussen 14y ago

"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 14y ago
It's all a simulation!

Tycho 14y ago

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 14y ago
Not energy, but entropy.