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What 'Negative Temperature' Really Means 204

Posted by Soulskill
from the not-a-car-analogy dept.
On Friday we discussed news of researchers getting a quantum gas to go below absolute zero. There was confusion about exactly what that meant, and several commenters pointed out that negative temperatures have been achieved before. Now, Rutgers physics grad student Aatish Bhatia has written a comprehensible post for the layman about how negative temperatures work, and why they're not actually "colder" than absolute zero. Quoting: "...you first need to engineer a system that has an upper limit to its energy. This is a very rare thing – normal, everyday stuff that we interact with has kinetic energy of motion, and there is no upper bound to how much kinetic energy it can have. Systems with an upper bound in energy don’t want to be in that highest energy state. ...these systems have low entropy in (i.e. low probability of being in) their high energy state. You have to experimentally ‘trick’ the system into getting here. This was first done in an ingenious experiment by Purcell and Pound in 1951, where they managed to trick the spins of nuclei in a crystal of Lithium Fluoride into entering just such an unlikely high energy state. In that experiment, they maintained a negative temperature for a few minutes. Since then, negative temperatures have been realized in many experiments, and most recently established in a completely different realm, of ultracold atoms of a quantum gas trapped in a laser."
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What 'Negative Temperature' Really Means

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  • Layman (Score:4, Insightful)

    by Anonymous Coward on Saturday January 05, 2013 @09:08PM (#42491705)

    I do not think this word means what you think it means.

    • Re:Layman (Score:5, Funny)

      by Biff Stu (654099) on Saturday January 05, 2013 @10:46PM (#42492301)

      layman
      n.
      A man who gets laid. Also known as a non-Slashdotter.

    • by mrops (927562)

      or maybe it does

      you will never know until you look inside the box... errr RTFA

    • by AdamWill (604569)

      What, you couldn't understand that? It's perfectly simple! Here, let me summarize: words words words words spin words words words negative words words words FRICKIN LASER

    • The article IS for the layman. The quote is not really representative for its general style.
    • Re:Layman (Score:4, Informative)

      by ByteSlicer (735276) on Sunday January 06, 2013 @08:04AM (#42494499)

      Here's my take on a layman explanation:

      It's a water model in the classical world. It doesn't model everything from the quantum world, but makes it easier to understand the concepts.

      Imagine a long vertical tube, closed off at the bottom.
      When it's empty, it has minimal entropy (a measure for the amount of disorder).
      When you add an amount of water (which models energy here), the water level rises and so does the entropy.

      Now the definition of temperature is amount of heat energy per amount of entropy (T=dQ/dS). In the above situation, both amounts are positive, so the temperature is also positive.

      Now imagine we close off the tube at the top too. This will leave an amount of air trapped there.
      When we add an amount of water (using a valve to make sure the air doesn't escape), at first the system will behave exactly the same.
      But when the water level gets near the top, the air gets pressurized and starts pushing back. And this increasingly so until it's almost full.

      If we would make a hole in the middle of the tube, the water would squirt out until a pressure equilibrium was reached. We could extract work from this, to power a little water wheel. This means the "full" state had a lower entropy than the "middle" state.

      So in this system, entropy went from a low value to a certain (maximum) higher value, and then back to a low value. This for an increasing amount of water (low, medium, max).

      So what does this mean for temperature as defined above?

      We kept adding the same amount of water (dQ in our model).
      The change in entropy (dS) this caused is the slope of a hill (low, max, low), so at first it is a positive amount, which gets smaller and smaller, to become zero at the equilibrium point. After that, adding more water (energy) will cause the entropy to go down again, so dS will become a small negative amount at first and a larger negative amount near "full".

      When we plug this in in the equation for temperature (T=dQ/dS) we get:

      Going from "empty" to "middle": dQ is positive and the same, dS is positive and gets smaller, approaching zero. So T starts at some positive value, then gets higher and higher approaching positive infinity.

      Going from "middle" to "full": dQ is still positive and the same, the change in entropy dS is zero at first and then becomes smaller and smaller (negative). So T starts out at negative infinity and then gets higher and higher approaching some negative value.

      This illustrates how the temperature scale goes for increasing heat energy:
      +0 ... +inf -> -inf ... -0

      So a system with negative temperature has more energy than the same system with any positive energy.

      • So a system with negative temperature has more energy than the same system with any positive temperature.

        FTFM :)

      • by vlm (69642)

        Now the definition of temperature is amount of heat energy per amount of entropy (T=dQ/dS).

        My version of the "laymans explanation" would revolve around that. There are several ways to define temperature, or at least several equations from distant corners of physics with a "T" in them where a bit of algebra can isolate that "T" to the left side all alone. At "normal human temperatures" those different ways to calculate a "T" all match up. Hopefully you're not surprised that at extremes of size (like astronomically large or atomic small) or extremes of ... (dramatic pause) temperature ... the eq

  • by Anonymous Coward

    kudos souskill

  • by Anonymous Coward

    At least nowadays. Plenty of lasers around.

    • by c0lo (1497653)

      Plenty of lasers around.

      No, lasers are not an example of negative temperature.

      For a thermodynamic system, zero temperature is when you can't vary (as in... decrease it) the internal energy of the system, the order of system is maximum.
      For a "negative temperature system" (no longer a thermodynamic one), this translates into "after a point, one can no longer pump energy into the system, the order has reach the maximum". This does not happen into a laser.

      • For a thermodynamic system, zero temperature is when you can't vary (as in... decrease it) the internal energy of the system, the order of system is maximum.

        For a "negative temperature system" (no longer a thermodynamic one), this translates into "after a point, one can no longer pump energy into the system, the order has reach the maximum".

        This is ... inexact.

        A zero temperature system is one where energy fluctuations are zero. Or, if you want the third principle definition, is a system with zero entropy. This will immediately tell you why you cannot reach absolute zero - you have to lose not only thermodynamic fluctuations, but quantum ones as well, which is impossible.

        A negative temperature system, otoh, is one where you have a population inversion on the energy level distribution. The elementary case is a 2-level system where the higher energy level has a higher occupation than the lower one. In order to follow the appropriate statistical distribution (M-B, B-E or F-D, depending on the system) the temperature has to be negative. The transition happens through the point of equal occupation, which corresponds to 1/T = 0, so T "wraps around" through infinite temperature (a theoretical construct, as you pointed out further down in the thread).

        What you are describing is a system who has *all* its components in the higher state (so that no more energy can be pumped, as there's nothing left to absorb it). This is indeed a case of negative temperature, but a trivial writing down of its distribution will let you know that you are at T = -0 (or 1/T = - infinity), which is as impossible to achieve in practice as the T = +0 case.

  • Uhhhh (Score:4, Interesting)

    by Anonymous Coward on Saturday January 05, 2013 @09:13PM (#42491741)

    This doesn't really help. I pondered this for a while the other day when I read that first and gave up trying to wrap my head around it. I was always under the impression that 0 kelvin (absolute 0) meant a state at which there was no movement at the atomic/subatomic level. It would seem as though to reach a negative temperature, one would have to slow a substances particles to less than 0 movement. Then I realized they were talking about a quantum state and I pretty much gave up trying to understand it at that point, because anything which has the word 'quantum' in it suddenly defies all the rules I'd ever been taught about anything at all. :o)

    • by alphatel (1450715) *
      Did you know also that light cannot escape a black hole?
      • by yusing (216625)

        Did you know that that idea is doomed to remain a purely hypothetical supposition, since (without a re-definition of 'black hole') there is utterly no way to test the idea??

    • Re:Uhhhh (Score:5, Insightful)

      by cwebster (100824) on Saturday January 05, 2013 @09:22PM (#42491807)

      All quantum means is that energy can only have specific values. Imagine a stereo with a volume knob that clicks between values, ie it can be 1, 2, 3, n, but cannot be anything inbetween those numbers. Now you have a quantum volume knob.

      Temperature is a statistical property of matter that only exists once we consider things as a continuum. At scales where we consider quantum mechanics, a molecule has energies (kinetic, rotational, vibrational, electrical, etc) which can only take on specific values (quantized) and these values are specific to the atom/molecule to some degree (atom makeup, radiative properties, etc).

      That probably doesnt help wtih the sub-0 part of the article, but perhaps it will help with the quantum part.

      • Re: (Score:3, Funny)

        by binarylarry (1338699)

        awesome, im totally buying that $2500 quantum volume knob from Monster Audio now. I bet it sounds amazing!

      • "It's very special, because as you can see, the numbers all go to -1, right across the board".

      • Re:Uhhhh (Score:5, Insightful)

        by hairyfeet (841228) <bassbeast1968@gm[ ].com ['ail' in gap]> on Saturday January 05, 2013 @10:53PM (#42492341) Journal

        That still doesn't explain how in the fuck you get below zero movement, how can you move less than none? For those that haven't seen it I suggest the excellent PBS documentary "The search for absolute zero" which is easy enough to find on the web where the second half deals with nothing but the attempts to reach absolute zero. in that video the scientists explain quite plainly that the reason its so damned hard to get those last couple of degrees out of the system is because you ALL movement from the medium has to be removed, not a single atom can move because movement is energy and absolute zero is the absolute absence of ALL energy.

        So sorry, still don't get it, its not like you can magically remove something from nothing. Absolute zero is absolute nothing, no energy left it the system at all, so how in the fuck are you gonna get less than nothing?

        • Re:Uhhhh (Score:5, Informative)

          by martin-boundary (547041) on Saturday January 05, 2013 @11:24PM (#42492489)

          That still doesn't explain how in the fuck you get below zero movement, how can you move less than none?

          The short answer is that physicists throw out the "temperature describes amount of molecular movement" definition and replace it with something more abstract.

          The abstract definition of temperature allows negative values, and that's ok because nobody cares anymore about molecular movements in that case.

          • Which is unfortunate, since the word "temperature" predates modern physics by centuries.
            The original meaning was the average speed of the molecules in a sample of matter - not atoms or subatomcs particles. Since speed is the length of a velocity vector, it cannot be negative, and hence there is no such thing as a negative temperature. It's a shame that physicists were too lazy to invent a new word for "slope of the entropy vs. energy curve" and decided, instead, to recycle - and corrupt - the meaning of a
            • by a whoabot (706122)

              The English word "temperature" was used in 1531 by Sir Thomas Elyot, long before Robert Boyle wrote The Sceptical Chymist. So how could that be its original meaning?

              • by eggstasy (458692)

                The word "temperature" comes from the Latin "temperatura", which is still the same word in Portuguese, Spanish, and Italian. It comes from "temperare", which means "to season" (food). Much like you mix herbs and spices in your food to achieve a desired taste, you mix cold water with hot water to achieve a desired temperature.
                Latin is only 2000 years old, I'm sure you could trace it back even further. The Proto-Indo-European root *tep- means "warm" (as in tepid), I'm not a linguist, though.

        • by mysidia (191772)

          That still doesn't explain how in the fuck you get below zero movement, how can you move less than none?

          Read the article for explanation. You indeed cannot have below zero "movement" or "jiggling". Negative temperature, says nothing about movement. That is the definition of temperature does not involve the amount of movement.

          That is, Temperature is not exactly equivalent to a measure of movement; there are things stated to have temperature where no notion of movement occurs; things like the magnetic s

          • Temperature (Score:5, Informative)

            by slew (2918) on Sunday January 06, 2013 @03:18AM (#42493441)

            Actually, it's not to hard to intuitively understand negative temperature if you think of it as something hotter than the hottest possible temperature. Classically, that isn't possible, but then you need a bit of quantum weirdness.

            In a typical system of normal temperature particles of occupy various quantum energy levels available to them. In thermal equilibrium, statistically, lower energy levels tend to get occupied first and higher energy levels have fewer particles. If somehow you can create a stable system where higher energy states are occupied, but by some quirk (of quantum mechanics), lower ones are not, it turns out that is what a negative temperature system is.

            As it turns temporarily creating a system where the higher energy levels are occupied before the lower ones is something that people do all the time to create a pumped laser. But lasers aren't designed to be a stable system (you eventually want the higher energy state to emit light/photons and fall to the lower energy state), so although the population of the energy states are inverted (more in the upper energy states), it's not stable, so it's generally not accurate to call this a negative temperature system.

            The reason the "sign" of the temperature is negative is just a problem with the definition of temperature. For most defintions of temperature, if you add energy, you increase entropy, so temperature is a measure of how these relate to each other (the slope). If somehow when you add energy to your system, you decrease entropy of your system (e.g, you pack the upper energy states even tighter reducing entropy instead of just letting particles in all energy states into statistically higher energy states), the slope is negative.

        • Re:Uhhhh (Score:5, Informative)

          by OneAhead (1495535) on Sunday January 06, 2013 @12:43AM (#42492869)
          It's just a quirk in our temperature scale. What we define as infinite K is not the highest-energy state that can be reached. It's the highest state that can be reached through heating, but higher states can be reached through other mechanisms. Once we realized that, we needed another scale for the higher-energy states at the other side of infinity, so we started using negative numbers for them. So negative temperatures are not at the cold side of 0K, but at the hot side of inifinity K. More complete explanations here [wikipedia.org] and here [slashdot.org].
        • by AK Marc (707885)
          You create a system where the material can absorb more heat than something at absolute zero can. It is, by regular definitions, "colder" than absolute zero, as it can absorb more heat. Yet, it is also more engergetic, thus "hotter". And being hotter and colder at the same time is confusing, so the creators call it negative. Don't think of it as colder than absolute zero, for if you define colder as the absence of heat, it is colder than absolute zero, but if you define hotter as having more energy, it's
      • Maxwell-Boltzmann statistics, and the field of statistical mechanics in general, work quite well with quantized systems. As an example, if you look at Boltzmann's definition of entropy: S = k ln W, where W is the possible number of microstates that can contribute to the system, you can see how statistical mechanics does a good job of handling quantized energy levels. Likewise, the Maxwell-Boltzman distribution does a fine job of describing the population distribution of an equilibrium ensemble of molecules

    • by kaws (2589929)
      Don't worry, just skim the article again because the claim isn't making temperatures go below absolute 0. Negative temperatures mean something completely different. My understanding is with negative temps, reverse what happens to water when you add energy. In other words, it's like heating up water but then the water starts to freeze. As you add energy to a negative energy system, it becomes more organized.
      • by Anonymous Coward

        Think of temp behaving as if it worked based on an absolute value (you know the whole |x| notation). As you add energy to a negative system (i.e. |-x+2|), it behaves as if you subracted energy from a positive one (|x-2|) because in absolute terms it is the same.

    • This doesn't really help. I pondered this for a while the other day when I read that first and gave up trying to wrap my head around it. I was always under the impression that 0 kelvin (absolute 0) meant a state at which there was no movement at the atomic/subatomic level. It would seem as though to reach a negative temperature, one would have to slow a substances particles to less than 0 movement. Then I realized they were talking about a quantum state and I pretty much gave up trying to understand it at that point, because anything which has the word 'quantum' in it suddenly defies all the rules I'd ever been taught about anything at all. :o)

      That was my first reaction when I learned about quantum mechanics - nothing fundamentally works the way I was taught it works, it only appears to work that way under certain conditions.

      Though, for this article, my first reaction was And the relevance of this discovery (again) is what, exactly? I didn't understand it before, I don't understand it now, and I don't see how it makes any difference what-so-ever.

    • Sounds to me like absolute zero means absolute zero temperature. But objects at absolute zero still retain energy, other than kinetic energy. One you reach absolute zero, those objects dig deep to find energy to give away, somehow converting that energy into heat, or kinetic energy.

      Maybe what we need here is a new form of measurement, something like "absolute energy" rather than "absolute temperature". If/when an object reaches absolute zero energy, what happens? I guess all the matter has been converte

    • Re:Uhhhh (Score:5, Informative)

      by Livius (318358) on Saturday January 05, 2013 @10:27PM (#42492225)

      The point they're making is that temperature can refer to energy and entropy other than just the kinetic motion kinds.

      Unfortunately understanding the definition still doesn't get us very far for those of us without intuitive models of those other kinds of situations, so we're no farther ahead.

    • Re:Uhhhh (Score:5, Informative)

      by Anonymous Coward on Saturday January 05, 2013 @10:28PM (#42492235)
      Stop thinking of temperature as the energy of a system, but think of it as the Maxwell–Boltzmann distribution of energy of the system. Certain temperature - certain shaped distribution. Bung in a temperature value, get out a distribution shape. Now, muck with the energy distribution such that the number input to the Maxwell–Boltzmann function to get that shape is negative. There you go, negative "temperature" while there's still energy in the system.
    • by LordCrank (74800)

      This doesn't really help. I pondered this for a while the other day when I read that first and gave up trying to wrap my head around it. I was always under the impression that 0 kelvin (absolute 0) meant a state at which there was no movement at the atomic/subatomic level. It would seem as though to reach a negative temperature, one would have to slow a substances particles to less than 0 movement. Then I realized they were talking about a quantum state and I pretty much gave up trying to understand it at t

    • by c0lo (1497653)

      This doesn't really help. I pondered this for a while the other day when I read that first and gave up trying to wrap my head around it. I was always under the impression that 0 kelvin (absolute 0) meant a state at which there was no movement at the atomic/subatomic level. It would seem as though to reach a negative temperature, one would have to slow a substances particles to less than 0 movement)

      My understanding on negative temperature [wikipedia.org] without requiring QM:

      1. in the classical thermodynamics and forcing the terms, the temperature is defined as "the measure of willingness of a system to un-aided transfer energy [wikipedia.org] to another system". If, when set in contact, two system do not exchange energy, they have the same temperature [wikipedia.org]. If one system spontaneously (i.e. not aided, without intervention) transfer energy to a second, then the temperature of the first one is higher than the second one

      2. you need to adj

    • by blueg3 (192743)

      You're thinking of "temperature" as only being a measure of the (average) kinetic energy of a collection of particles. However, in physics, it has a more general definition.

      So, the short answer to "it doesn't make sense to have less than zero motion" is that that's not what's happening at all. So no worries.

    • by OneAhead (1495535)
      Try this [slashdot.org]; it's a bit shorter and the quantum mechanics is masked as binary logic.
    • I found this article, linked at the bottom of TFA, much easier to understand: Leprechauns and Laser Beams [coffeeshopphysics.com].

    • by AK Marc (707885)
      Zero is zero. Zero energy, zero movement. But negative is a construct that contains more energy than absolute zero, but can also absorb more heat than absolute zero. That makes it more energetic (hotter), and "colder" at the same time. Quantum doesn't matter. That's just how they do it, not what it is.
  • I'm still not getting the definition of "temperature" here. As I read this it says "some matter in some states will get colder without giving it energy." How does this not go directly against the laws of physics by reversing entropy?
    • by OneAhead (1495535) on Sunday January 06, 2013 @12:56AM (#42492929)
      If you increase the average energy in certain types of quantum systems beyond a certain point, the entropy starts to go down again. Take a large number of ordinary binary bits and define the average energy as the number of 1s and the entropy as (the logarithm of) the number of combinations/binary numbers that have that many 1s. You'll see that there's only one combination for "all 0s" (entropy=0), the entropy peaks at "50% 1s", and then goes down again to reach 0 at "all 1s". I tried to explain that here [slashdot.org].
  • by rossdee (243626) on Saturday January 05, 2013 @09:36PM (#42491883)

    In the USA, it means its really, really cold, you'll have to dress well, including good gloves and hat. If there is any wind you'll wand to cover your face too.
    and the air is very dry, inside, getting a humidifier is a good idea.. If your car or truck has been parked outside for a while you would need to start it and have it warm up for 10 minutes before driving off.

    In the rest of the world its cold but bearable, since its just below freezing sidewalks may be slippery.

    • In the USA, it means its really, really cold, you'll have to dress well, including good gloves and hat. If there is any wind you'll wand to cover your face too. and the air is very dry, inside, getting a humidifier is a good idea.. If your car or truck has been parked outside for a while you would need to start it and have it warm up for 10 minutes before driving off.

      In the rest of the world its cold but bearable, since its just below freezing sidewalks may be slippery.

      So, what you're saying is that the canadian climate has below 0 temperatures for two reasons: The system of measurement is fundamentally flawed, and it's colder than we get in this area, normally.

  • Purcell and Pound (Score:5, Informative)

    by calidoscope (312571) on Saturday January 05, 2013 @09:40PM (#42491923)

    It would have been nice for Aatish to go a bit into what Purcell and Pound did in their 1951 experiment, namely "inverting" the orientation of the fluorine nuclei in the presence of an applied magnetic field by application of a radio frequency magnetic pulse, where the frequency is the Larmor frequency of fluorine and the pulse amplitude and length was sufficient to cause a 180 degree nutation. The result is that the nuclei have the same order (entropy) as the rest state, but have higher energy. In NMR, this is referred to as applying a 180 degree or pi pulse.

    Aatish's comment about reality being liberal is unconvincing.

    • Aatish's comment about reality being liberal is unconvincing.

      Only to the part of the population that isn't the 47%.

    • by TubeSteak (669689)

      Now, I know there are some polls out there saying this man [President George Bush] has a 32 percent approval rating. But guys like us, we don't pay attention to the polls. We know that polls are just a collection of statistics that reflect what people are thinking in reality. And reality has a well-known liberal bias.

      Stephen Colbert said this to President Bush's face at the 2006 White House Correspondents' Association Dinner.
      The joke that "reality has a well-known liberal bias" has since taken on larger meanings about Republican/Conservative ideas and ideology being divorced from reality and reality being biased towards liberal ideas because liberal ideas are more in tune with facts. See Also: Truthiness

      So why am I inventing this socialist utopia with rampant income redistribution? Itâ(TM)s because this is closely analogous to the physics of heat (as Steven Colbert put it, reality has a well know liberal bias).

      Socialist utopia with rampant income redistribution = his physics analogy = reality
      Does the joke make sense now?

  • by Anonymous Coward

    It just means the pressure pulls inwards rather than pushes outwards. Given given P=nRT, that would correspond to a negative temperature (since it means the pressure is negative (like a vacuum) and since n and R must be positive (being a count and a constant respectively), thus you can only get the negative sign from T (temperature). Never mind that baked into R (Rydberg Constant) there are assumptions that would exclude the current application and thus the "Negative Temperature" assertion, it's marketing,

    • Who modded this shit up?

      It is yet another person who refuses to read TFA and make random assertions.

      It basically amounts to saying he doesn't believe in negative temperatures because he doesn't like how the maths works out. Suck it.

  • Here! [wikipedia.org]

    a system with a truly negative temperature in absolute terms on the Kelvin scale is hotter than any system with a positive temperature. If a negative-temperature system and a positive-temperature system come in contact, heat will flow from the negative- to the positive-temperature system.

    That a system at negative temperature is hotter than any system at positive temperature is paradoxical if absolute temperature is interpreted as an average internal energy of the system. The paradox is resolved by understanding temperature through its more rigorous definition as the tradeoff between energy and entropy, with the reciprocal of the temperature, thermodynamic beta, as the more fundamental quantity. 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.

    You add more energy, but the entropy doesn't increase. Gods damn that moronic blogger and his useless "tricks" metaphor. You don't "trick" shit you stupid fuck. You wouldn't say gunpowder "tricks" a lead projectile to scurry from the gun barrel if you were explaining a gun. We're not idiots, we just need to have the terms defined because some of us hadn't heard the term before in relation to absolute zero.

    Protip: Next time you want to submit or vote up a "follow-up" fucking read the damn thing

  • by slashmydots (2189826) on Saturday January 05, 2013 @11:21PM (#42492467)
    So you give more energy to it to force it into a high energy state and that lowers its temperature even though it's more energy? Or you force the material to act like it's in a high energy state without giving it the energy so its amount of transmittable heat results in a math glitch? Either way, that's stupid and all it means is temperature isn't measured correctly. I'm in the minority who considers temperature to be total average speed that a group of atoms are moving at. Since that type of system can't drop below zero, I'd say it's superior.
    • by OneAhead (1495535)
      You're welcome to introduce your own temperature scale. It won't be a linear function of the existing temperature scales and will be very inconventient for practical purposes, though.
  • by drolli (522659) on Sunday January 06, 2013 @01:16AM (#42493019) Journal

    I thought about explaining it, and i will do so *without* mentioning the Dalai Lama.

    The Situation is very simple: The definition of Temperature you learned in school, namely that it is only related to the average energy of many equal systems *is right*, but only for *classical systems*.

    What does it mean?

    If i have a classical gas, e.g. air at room temperature and i have to input to it, i can add this energy in whichever distribution i want. Easy to do that, no matter at which temperature we are.

    No lets consider a quantum gas (to be complete: a quantum gas and not consiting of harmonic oscillators), e.g. electrons spins which are aligned to a magnetic field. Each of the electron can either have an Energy of -1/2E or +1/2E, where E depends on the electron spin and the magnetig field, but is constant. This means that if i have N electrons, we wont be able to input more energy than N * E into the system. Moreover if only a single electron in not in the high-energy state, we have to flip exactly this electron to get the system into its highest energy state. That may be pretty hard, statistically speaking.

    So now imagine a quantum gas somehow statistically exchanging energy with a classical gas. That means, in our case, to bring the quantum gas to the state of Total energy = N*E (from the state of (N-1)*E) a high energy gas molecule would have the hit the very last of the low-ebergy electrons. If the high-energy molecules bounce from the electron in the excited state, then nothing will happen.

    It is intuitive that, even if the two gases are in contact, the avergae energy between the systems will *not* be the same, just because its unlikely to flip *all* or *nearly all*.

    The fromal version if this consideration is the textbook definition of the Temperature as a property in statistical physics, which is T=dE/dS, where E is the total energy and S is the Entropy (yes, the very same one as in computational science).

    In the case of the two-level systems we find (let n be the numebr of systems in exited state)

    S is proportional to -(n*log(n/N) + (N-n)*log((N-n)/n))
    E is proprotioanl to n

    That means that the sign of the temperature changes, as soon as more systems are excited than not.

  • by AdamHaun (43173) on Sunday January 06, 2013 @03:38AM (#42493531) Journal

    There's a link in the article to Leprechauns and Laser Beams [coffeeshopphysics.com], which IMHO does a much better job of explaining things. As I understand it, negative temperatures don't just come from the entropy-based definition of temperature. You also need to be talking about a system whose energy content is capped. Normal materials don't do this -- you can keep adding energy (speeding up atoms) as long as you want. But if you have a group of atoms with exactly two energy states (high and low), once every atom is in the high-energy state you can't add more energy. Apparently, one example of this is a laser.

    From an entropy point of view, the lowest energy and highest energy states have identical entropy (i.e. none -- one possible state). Entropy reaches a peak with half of the atoms in the high energy state, since this gives the largest number of possible atom state combinations.

    Temperature is defined as the slope of the energy/entropy curve. The curve goes vertical at max entropy. If I understand right, at this point the temperature overflows like an integer variable, going from +inf to -inf and approaching zero from the negative end. (It's not really a continuous curve, but I don't know enough to guess at what difference that makes.)

    So it sounds like the recent news about a negative-temperature gas was more about creating a new material with these sorts of quantum states. The negative temperature part caught the attention of the reporters (and the rest of us), but isn't the real scientific discovery. That's my reading of it, anyway.

  • Do they have one for something less than a layman? Perhaps one written for a complete ignoramus like myself.

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