What is the Entropy at ZERO Degrees Kelvin?

[fxdung]

Planck states that all perfect crystalline system have the same entropy in limit T approaches zero,so we can put the entropy equal zero.Can we demonstrate that or is it only a presumption?

 

[fxdung]

Is there any experiment demonstrating this statement?

 

[Dale]

It can be derived from statistical mechanics. For statistical mechanics $S_0=k_B \ln \Omega_0$ where $S_0$ is the entropy at absolute zero and $\Omega_0$ is the number of microstates available at absolute zero. For a perfect crystal $\Omega_0=1$ so $S_0=0$.

 

[fxdung]

Can ground state degenerate,so that Omega_0 greater than 1?

 

[Dale]

Can ground state degenerate,so that Omega_0 greater than 1?

Yes in general, but not for a perfect crystal.

 

[fxdung]

Why in perfect crytal there is a unique ground state if we consider the complex structure of each vertex of lattice?

 

[fxdung]

May be we consider only a part of the entropy that relates with lattice vibrations?

 

[Dale]

Why in perfect crytal there is a unique ground state if we consider the complex structure of each vertex of lattice?

What “complex structure” are you talking about? A perfect crystal has only one ground state, is your "complex structure" referring to something other than the state, if so what?

 

[fxdung]

There are many types of lattice,each vertex has many types of atoms,each atom has electrons and nuclons and so on.Each of them has its own ground state.

 

[Dale]

But each atom has only one ground state. So why would the overall ground state not be unique?

 

[fxdung]

Why do we know all elementary particles that atom consist of do not degenerate in ground state?

 

[Dale]

No. Why would they? You keep avoiding this question. Please answer it directly. What do you believe would cause degeneracy here?

Also, some matter particles are bosons.

 

[fxdung]

Do you mean that matter particles do not degenerate at ground state?

 

[fxdung]

I do not know about QM saying of this things.So if we say not being degenerate,then I think we need a demonstration.

 

[Dale]

If it is degenerate then there is some operator that commutes with the Hamiltonian. As far as I know there is none for the Hamiltonian of a perfect crystal.

What operator do you believe commutes?

 

[fxdung]

Conductor electrons in crystal have conserved momentum!

 

[Dale]

Yes. And since $V\ne 0$ the momentum operator does not commute with the Hamiltonian in an ideal crystal. So there is no degeneracy for different momentum states.

 

[fxdung]

But there are many symmetries in crystal,so I think there are many observations that commute with Hamintonian(?)

 

[Dale]

Then it should be easy to find one. So again which operator do you believe commutes?

Since it is commonly claimed that the entropy of an ideal crystal is 0 because the ground state is unique, you are claiming that all those people are wrong. If you are making such an extraordinary claim you should back it up with extraordinary evidence. “I think there are many” is not.

Please study and find a scientific reference describing one of these many commuting operators. Until then this thread is closed.