# Is absolute zero really a lower bound?

I understand that temperature has a lower bound of zero kelvin. Is this temperature actually achievable. If not, isn't zero kelvin just acting like negative infinity?

For example, say I come up with a new temperature unit. It will be related to Kelvin by just being the log. So $t = \log(k)$, where t is the new temperature, and k is the temperature in Kelvin.

T can range from $-\infty$ to $\infty$, thus there is no lower bound to this temperature measurement.

Similarly, I can make $u = 1/2 + \arctan(\log(k))/\pi$ to get a temperature measurement (0, 1). So now there is an absolute hot of 1 and absolute cold of 0..

Is there a reason that Kelvin is much better? Is it true that temperature having a lower bound but no upper bound is just a matter of "perspective"? Or is there something inherent about temperature that I am missing?

• Temperature measures energy, which is useful. The logarithm of energy... not so much. I have no idea what you mean by logarithm of a unit. – CuriousOne Aug 10 '16 at 21:34
• I meant the variable K to be the value of the temperature in Kelvin. I see how that can be confusing since the unit is usually denoted by K. I will change the variables to lowercase to hopefully make it clearer. I guess the answer is usefulness of the unit. That answers my question I suppose. Thanks. – zrbecker Aug 10 '16 at 22:23
• Sort of. The real 'nice' variable is the inverse temperature $\beta = 1/k_B T$. That goes out to $+\infty$ instead of "stopping at zero", as you want. – knzhou Aug 10 '16 at 22:24
• Essentially a duplicate of physics.stackexchange.com/q/21851/2451 and links therein. – Qmechanic Aug 10 '16 at 22:52

At the risk of stating something you already know :

Is this temperature actually achievable?

The laws of thermodynamics dictate that absolute zero cannot be reached using only thermodynamic means, as the temperature of the substance being cooled approaches the temperature of the cooling agent asymptotically. A system at absolute zero still possesses quantum mechanical zero-point energy, the energy of its ground state at absolute zero. The kinetic energy of the ground state cannot be removed.

Or is there something inherent about temperature that I am missing?

It would seem from the except above, and the equations linking temperature with kinetic energy, that no matter what scale you devise, or transform an existing scale into, because ZPE is never equal to zero, the Kelvin scale is as good as any other.(And less complicated).

• I did read that quote. I guess I am still a little fuzzy on what they mean by "cannot be reached using only thermodynamic mean". This suggests that in theory zero can be reached by other means. I did not realize the temperature was just a measurement of energy. I thought we had other units for that. In this case if something measured zero kelvin, it would have zero energy. Is that something that is theoretically possible? Or do all things always have some amount of energy? – zrbecker Aug 10 '16 at 22:30
• Temperature is a measure of energy. If you could get an atom, or electron to sit still, it would still have its rest mass energy. Have a read of livescience.com/25959-atoms-colder-than-absolute-zero.html and Google laser cooling. Thermodynamic means, I read as any means, but I agree it could be written more clearly. – user108787 Aug 10 '16 at 22:44
• Thank is a very interesting looking article. I've just skimmed through it. Thanks. :D – zrbecker Aug 10 '16 at 22:48
• Your next question could be to read that article, and then ask on here, for an explanation of it, as it seems to contradict all the above, but I am sure there is an explanation for it. – user108787 Aug 10 '16 at 22:50