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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?

zrbecker
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At the risk of stating something you already know : 

Is this temperature actually achievable?

From Wikipedia Absolute Zero

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).

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