Relativistic effects at small temperatures

[Marin]

Hi all!

I'm doing a statistical mechanics class this semester where very often questions like "consider the limit of temperature going to..." pop up.

Now, if you consider a relativistic system (say some gas), to what extent does it make sense to talk about temperature going to 0? [to me, it's kind of counter-intuitive, since in the relativistic limit velocities are usually very high and thus the inner energy of the gas particles as well]

Are there any examples of ultra-cold relativistic systems?


Thanks for your contribution in advance

 

[tiny-tim]

Hi Marin!

Now, if you consider a relativistic system (say some gas), to what extent does it make sense to talk about temperature going to 0? [to me, it's kind of counter-intuitive, since in the relativistic limit velocities are usually very high and thus the inner energy of the gas particles as well]

I really don't see a problem here …

the temperature depends on the speed of the particles relative to the centre of mass (or to the average velocity) …

moving the whole thing near the speed of light won't change the relative motion: the temperature will stay the same

Are there any examples of ultra-cold relativistic systems?

Yup … any ultra-cold system as viewed by an observer moving away from it near the speed of light.

 

[kanato]

A Fermi gas which is filled to the point where speeds are nearly relativistic will still behave relativistically at zero temperature. Since two Fermions can't occupy the same state regardless of temperature, if you have enough of them to fill states up to relativistic velocities that can't change at low temperature.