Is Temperature Truly Quantized at Absolute Zero?

[UncertaintyAjay]

Right, so. A couple years ago, before I learned about electron orbitals etc. I sort of figured out that energy was quantized. I always thought that my logic was right, but you never know. So I'll outline my argument below and could someone tell me if its logically and physically sound? And if it isn't, why not?

So, I had just learned about 0 K being the lowest possible temperature and that matter was at its lowest energy at 0K. I also learned that things can't go below this temperature because they can't have 0 energy.
Ergo, if something were to go even an infinitesimal bit below 0K, it would have zero energy. But an infinitesimal temperature change would lead to an infinitesimal energy change. Since this is not allowed, temperature must change in some multiple of some number, call it T. Obviously, at 0K matter must have some energy, call it E. So, the only allowed temperature change will be that which would result in an energy change of magnitude E. So, if temperature were to drop below 0K, the first allowed temperature change would result in an energy decrease of E. Which is why temperature would never fall below 0K. So any energy change must be an integral multiple of E and any temperature change an integral multiple of T.

 

[Drakkith]

Ergo, if something were to go even an infinitesimal bit below 0K, it would have zero energy.

Note true. Absolute zero is a minimum energy state, but it is not a zero energy or even a near-zero energy state.

Ergo, if something were to go even an infinitesimal bit below 0K, it would have zero energy. But an infinitesimal temperature change would lead to an infinitesimal energy change. Since this is not allowed, temperature must change in some multiple of some number, call it T. Obviously, at 0K matter must have some energy, call it E. So, the only allowed temperature change will be that which would result in an energy change of magnitude E. So, if temperature were to drop below 0K, the first allowed temperature change would result in an energy decrease of E. Which is why temperature would never fall below 0K. So any energy change must be an integral multiple of E and any temperature change an integral multiple of T.

Temperature is (generally) not quantized. Not for macroscopic systems at least.

 

[UncertaintyAjay]

No, I'm aware that 0K is anything but a zero energy state. I suppose the root of my confusion lies in the fact that I was never explained why 0 Kelvin is the lowest possible temperature. Could you clarify this.

 

[DrClaude]

Historically, 0 K was set by the observation that for (ideal) gases, there is a limit in a P vs T plot where $P \leftarrow 0$, and that limit can be set as $T = 0$, which defines an absolute temperature scale. Considering that in gases energy is essentially kinetic energy, this limit has a need physical explanation as the point where the kinetic energy is zero.

Adding interactions or internal degrees of freedom, we get that T = 0 K also corresponds to the ground state of the system, where QM tells us that there is residual (zero-point) energy. But the ground state is the ground state, so the system can't go lower.

That said, the modern definition of temperature is
$$
\frac{1}{T} = \frac{\partial S}{\partial U}
$$
Generally speaking entropy varies in the same direction as energy, so $T>0$, but there exists systems that can have a negative temperature. Note though that they correspond to systems that are hotter than $T = \infty$; i.e., energy will flow from a negative temperature object into any positive energy object.

Also, temperature is a statistical property. I don't see how it could be quantized.