# Is it theoretically possible to reach $0$ Kelvin?

By the third law of thermodynamics, a quantum system has temperature absolute zero if and only if its entropy is zero, i.e., if it is in a pure state.

Because of the unavoidable interaction with the environment this is impossible to achieve.

But it has nothing to do with all molecules standing still, which is impossible for a quantum system as the mean square velocity in any normalized state is positive.

I think you are both wrong.

"The lowest energy state still has non-zero energy" does not mean that the temperature cannot be zero. If the system is in the ground state with 100% probability, then the temperature is zero. It doesn't matter what the ground state energy is.

It's true that all molecules in the substance would stand perfectly still at absolute zero [well, they don't have exact positions by the uncertainty principle, but the probability distribution of position would be perfectly stationary]. But so what? Why would that make absolute zero impossible? [see update below]

Nevertheless, there is no process that can get a system all the way to absolute zero in a finite amount of time or a finite number of steps. There's just no way to get that last little bit of energy out. This is one aspect of the third law of thermodynamics, as discussed in some (but not all) thermodynamics textbooks.

-- UPDATE --

It seems likely that I misunderstood. By "stand perfectly still", I guess you meant "have a fixed and definite position, and a fixed and definite velocity equal to 0". If that's what you meant, then "standing perfectly still" is indeed impossible (because of the Heisenberg Uncertainty Principle). But "standing perfectly still" is not expected or required to happen at absolute zero. Again, a harmonic oscillator which is in the ground state with 100% probability is at absolute zero, but does not have fixed and definite position or velocity.

from WP-negative temperature

In physics, certain systems can achieve negative temperature; that is, their thermodynamic temperature can be expressed as a negative quantity on the kelvin scale.

A substance with a negative temperature is not colder than absolute zero, but rather it is hotter than infinite temperature. As Kittel and Kroemer (p. 462) put it, "The temperature scale from cold to hot runs: +0 K, . . . , +300 K, . . . , +∞ K, −∞ K, . . . , −300 K, . . . , −0 K."

. The inverse temperature β = 1/kT (where k is Boltzmann's constant) scale runs continuously from low energy to high as +∞, . . . , −∞.

from Positive and negative picokelvin temperatures :

... of the procedure for cooling an assembly of silver or rhodium nuclei to negative nanokelvin temperatures.