Negative Temperatures: Understanding the Impossible

[LURCH]

[mentor's note: this thread has been split off from this one.

This isn't my gig, but negative temperatures are mainsteam physics. I don't know if zero is included.

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

A very interesting article.

In particular, it may take me sometime to understand the statement:

a system with a truly negative temperature is not colder than absolute zero; in fact, temperatures colder than absolute zero are impossible.

At first, I thought this was going to be an article relating to "negative energy." But, they are talking about a negative absolute temperature throughout a particular system.

 

[mgb_phys]

Remember it's only a negative temperature for a particlular way of defining temperature!
Sometimes in physics it's convenient to twist 'normal' definitions in unusual circumstances to allow you to carry on using the same laws and equations.

A good example is in semiconductors, electric chargeis carried by -ve charged electrons, but it's often more convenient to think in terms of missing electrons giving a local positive charge. To do this you talk about the movement of 'holes' an imaginary positive charged particle that is (in simple terms) the absence of an electron.

 

[Phrak]

Remember it's only a negative temperature for a particlular way of defining temperature!
Sometimes in physics it's convenient to twist 'normal' definitions in unusual circumstances to allow you to carry on using the same laws and equations.

Are negative temperatures inconsistant with some ways in which temperature is defined?

 

[GTOzoom]

negative temperatures are just negative on the scale you measure them. When they say that nothing can have a negative temperature they are talking in Kelvin's.

Heat is merely molecular motion, so if there is a lack of all motion in an atom it is in its ground state, at absolute zero. Since it can't have 'negative' motion there can't be a negative temperature on the kelvin scale, by definition its impossible.

 

[schroder]

negative temperatures are just negative on the scale you measure them. When they say that nothing can have a negative temperature they are talking in Kelvin's.

Heat is merely molecular motion, so if there is a lack of all motion in an atom it is in its ground state, at absolute zero. Since it can't have 'negative' motion there can't be a negative temperature on the kelvin scale, by definition its impossible.

Yes, but if you read the article, these people are talking about Kelvins! It has always been my understanding that absolute zero is the limit of all temperatures, -273.15... C, or 0 Kelvin and is a temperature one can never reach or measure as all nuclear activity is at ground zero state. As best I can determine, the current record low temperature is 100 pK, or 0.000 000 000 1 degrees above the absolute zero. This was achieved by researchers of the YKI-group of the Low Temperature Laboratory in Finland a few years ago. Possibly this has been exceeded somewhere else but I find it incredible that there are claims being made for negative temperature measured in Kelvin! This must be based on some different definition of temperature, other than a true thermal equilibrium being reached. Reading through the links, it seems to me the explanation involves flipping the nuclear poles in a tiny sample of rhodium to simulate ferromagnetic properties which are somhow associated with “negative” temperature. This strikes me as a bit of sleight of hand, as even the researchers note: “Since heat is transferred from the warmer to the colder part when two systems are brought into thermal contact, negative temperatures are actually hotter than positive ones.” So this claim is not based on any normal criteria for thermal activity. I also came across this comment: “In a certain sense, the system passes from positive to negative temperatures via T = + 0 to T = - 0 without crossing through the absolute zero. Therefore, the third law of thermodynamics is not invalidated.” So, does it cross into negative territory by passing through infinity, and if so, where does the infinite energy come from? I suppose if you change the goal posts and redefine the game, you can claim anything you like, but I do not see anything here that can be called negative temperature.

 

[LURCH]

I just realized that my comment about negative energy needs clarification. Negative energy and a negative absolute temperature throughout a system are mutually exclusive concepts because any system that harbours negative energy must also contain a greater amount of positive energy.

Remember it's only a negative temperature for a particlular way of defining temperature!
Sometimes in physics it's convenient to twist 'normal' definitions in unusual circumstances to allow you to carry on using the same laws and equations.

Yeah, that's the impression I got. I understand that one can define "negative temperature" as the condition of any system which, when brought into contact with another system, will lose energy to that other system. However, this does bring up further questions (BTW; thanks Mods for splitting this off as a separate thread) like, "how can a colder system lose energy to a warmer one?" and "if that can happen, what now is the barrier to reaching Absolute Zero?" Obviously, I need to research the idea further, but if I'm reading the article correctly, as the system with "negative temperature" loses energy, it will suddenly jump to a state of higher energy. This is a difficult concept to grasp, but it sounds to me rather similar to the idea in M-theory in which, at very small distances, contraction can become expansion. Are the two as simillar as they seem?

 

[LURCH]

Yes, but if you read the article, these people are talking about Kelvins! It has always been my understanding that absolute zero is the limit of all temperatures, -273.15... C, or 0 Kelvin and is a temperature one can never reach or measure as all nuclear activity is at ground zero state. As best I can determine, the current record low temperature is 100 pK, or 0.000 000 000 1 degrees above the absolute zero. This was achieved by researchers of the YKI-group of the Low Temperature Laboratory in Finland a few years ago. Possibly this has been exceeded somewhere else but I find it incredible that there are claims being made for negative temperature measured in Kelvin! This must be based on some different definition of temperature, other than a true thermal equilibrium being reached. Reading through the links, it seems to me the explanation involves flipping the nuclear poles in a tiny sample of rhodium to simulate ferromagnetic properties which are somhow associated with “negative” temperature. This strikes me as a bit of sleight of hand, as even the researchers note: “Since heat is transferred from the warmer to the colder part when two systems are brought into thermal contact, negative temperatures are actually hotter than positive ones.” So this claim is not based on any normal criteria for thermal activity. I also came across this comment: “In a certain sense, the system passes from positive to negative temperatures via T = + 0 to T = - 0 without crossing through the absolute zero. Therefore, the third law of thermodynamics is not invalidated.” So, does it cross into negative territory by passing through infinity, and if so, where does the infinite energy come from? I suppose if you change the goal posts and redefine the game, you can claim anything you like, but I do not see anything here that can be called negative temperature.

What they are claiming, though, is that they have achieved a "negative temperature," on the Kelvin scale, but not "colder than zero."

 

[atyy]

Only systems that have a finite number of energy states have negative temperatures.

The definition is made using the microcanonical ensemble and the second law definition of temperature.

A negative temperature is hotter than absolute zero in the sense that more than one microstate corresponds to a macrostate with negative absolute temperature.

Or something like that ... I don't remember exactly.

 

[Phrak]

Like I said, this stuff in not my gig. But I scanned the Wiki article and it defines--or redefines temperature as

$$T = fract{dq_{rev}}{dS}$$

The temperature is equal to the energy added to the system per the increase in entropy.

But look at this equation. It's a quantity defined as a derivative. It begs for a constant of integration, or in more lelevated-brow terms, a (what's the term?) a regauging.

Perhaps the negative-energy crowd should be qualifying the "field" phi, that such that

$$T = \frac{dq_{rev}}{dS} + \phi$$

 

[Phrak]

Like I said, this stuff in not my gig. But I scanned the Wiki article and it defines--or redefines temperature as

$$T = \frac{dq_{rev}}{dS}$$

The temperature is equal to the energy added to the system per the increase in entropy.

But look at this equation. It's a quantity defined as a derivative. It begs for a constant of integration, or in more-high brow terms, a regauging.

Perhaps the negative-energy crowd should be qualifying the T_{strange} field, that such that

$$T = \int \frac{1}{S} dq_{rev} - T_{strange}$$

where T is the usual definition of temperature.

 

[atyy]

Only systems that have a finite number of energy states have negative temperatures.

The definition is made using the microcanonical ensemble and the second law definition of temperature.

A negative temperature is hotter than absolute zero in the sense that more than one microstate corresponds to a macrostate with negative absolute temperature.

Or something like that ... I don't remember exactly.

Here's a more correct (I think) version.

In the microcanonical ensemble:
S=klog(w),
S=entropy
k=Boltzmann constant
w=number of states with given energy

From classical thermodynamics, 1/T=(dS/dE)_N

In most systems, as energy increases, the number of states available increases.

In a two state system, as energy increases, the number of states available decreases.

Once a two state system is brought in contact with a normal system that does not have a maximum energy, it will lose its excess energy and come to equilibrium at a positive temperature.

Mehran Kardar, Lecture 12:
http://ocw.mit.edu/OcwWeb/Physics/8-333Fall-2005/CourseHome/index.htm

John Denker, Chapter 9:
http://www.av8n.com/physics/thermo-laws.htm