# Negative temperature and entropy

1. Feb 22, 2013

### persia7

we know the entropy in each process increases is it true for absolute negative temperature?

2. Feb 22, 2013

### Naty1

3. Feb 22, 2013

### persia7

a week ago scientist discover there is negative temperature,if you suppose there is, what is your answer?

4. Feb 22, 2013

### Vagn

The negative temperature arrives from the definition of temperature.

So if the entropy of the system decreases with increasing energy, then the temperature is said to be negative. This is common in lasers, where population inversion can be considered as a negative temperature.

5. Feb 22, 2013

### Cthugha

Negative temperature has been known for a far longer time now. I think it was the first demonstration of negative temperature for an atomic gas which has been published recently. Here adding energy can decrease entropy. However, it is important to note two things:

1) Although the temperature is negative, one cannot translate that into the system being colder than one at absolute zero. It is instead VERY hot.

2) Negative temperatures occur in metastable or quasi-equilibrium systems, NOT in systems which are in equilibrium, so you keep a state stable which is not the ground state. You may imagine such state as similar to the steady state of a laser which involves population inversion. Note the difference between steady state and equilibrium state! As these states are not the equilibrium ones, you do not run into trouble with thermodynamics.

6. Feb 22, 2013

### persia7

the principle increasing of entropy is universal , please explain it in negative temperature.

7. Feb 22, 2013

### QuasiParticle

Well, they are metastable only in the sense that their environment is colder, thus they tend to cool (go toward positive temperatures). This is true for any system (positive or negative temperature), which is hotter than its surroundings.

Some systems (e.g. nuclear spins in magnetic field) can be decoupled from their environment so effectively that a negative temperature remains even days without any additional work.

8. Feb 22, 2013

### Cthugha

Well almost, it applies to isolated systems only, but that qualifies as universal in my opinion. You only get negative temperatures for systems with a limited number of states. Think about the omnipresent spins in a magnetic field. The ground state (temperature 0 if you wish) consists of all spins aligned with the magnetic field. There is only one microstate for this configuration. Now the highest entropy comes up when half of the spins are aligned along the field and half of them are aligned contrary to it. There are many microstates for this configuration. Now a higher energy state is given when all spins are aligned contrary to the magnetic field. Interestingly, there is again only one microstate for this configuration, so the entropy is low. As entropy decreased by adding energy, this corresponds to negative temperature. If you just let this system evolve, it can only go to states with higher entropy as it is already the state of lowest entropy, so there is no problem with thermodynsmics.

This is of course correct. In principle they may be as metastable as glass, for example.

9. Feb 23, 2013

### persia7

is clausius inequality correct for negative temperature?, if you see the proof of it in positive temperature its not correct.