What is the Entropy at ZERO Degrees Kelvin?

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Discussion Overview

The discussion revolves around the concept of entropy at absolute zero, specifically in relation to perfect crystals. Participants explore theoretical implications, statistical mechanics, and the nature of ground states in crystalline structures.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants reference Planck's assertion that perfect crystalline systems have zero entropy at absolute zero, questioning whether this can be demonstrated or is merely a presumption.
  • There is a request for experimental evidence supporting the claim that the entropy of a perfect crystal is zero at absolute zero.
  • One participant proposes a derivation from statistical mechanics, stating that for a perfect crystal, the number of microstates at absolute zero is one, leading to zero entropy.
  • Questions arise regarding the possibility of ground state degeneracy, with some participants suggesting that it could lead to a non-zero number of microstates.
  • Discussion includes the complexity of lattice structures and whether this complexity affects the uniqueness of the ground state in perfect crystals.
  • Participants debate the implications of atomic structure and the nature of elementary particles in relation to ground state degeneracy.
  • There are assertions that in a perfect crystal, each atom has a unique ground state, leading to the conclusion that the overall ground state should also be unique.
  • One participant challenges the notion of degeneracy, asking for clarification on what would cause it in the context of perfect crystals.
  • The role of symmetries in crystals and their relationship to commuting operators with the Hamiltonian is discussed, with some participants expressing skepticism about the existence of such operators that would indicate degeneracy.

Areas of Agreement / Disagreement

Participants express differing views on the uniqueness of the ground state in perfect crystals and the implications for entropy at absolute zero. The discussion remains unresolved, with multiple competing perspectives on the nature of degeneracy and the validity of existing claims.

Contextual Notes

Participants note the complexity of lattice structures and the potential for various interpretations of ground state degeneracy, which may depend on specific definitions and assumptions not fully explored in the discussion.

fxdung
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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?
 
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Is there any experiment demonstrating this statement?
 
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##.
 
Can ground state degenerate,so that Omega_0 greater than 1?
 
fxdung said:
Can ground state degenerate,so that Omega_0 greater than 1?
Yes in general, but not for a perfect crystal.
 
Why in perfect crytal there is a unique ground state if we consider the complex structure of each vertex of lattice?
 
May be we consider only a part of the entropy that relates with lattice vibrations?
 
fxdung said:
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?
 
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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.
 
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  • #10
But each atom has only one ground state. So why would the overall ground state not be unique?
 
  • #11
Why do we know all elementary particles that atom consist of do not degenerate in ground state?
 
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  • #12
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.
 
  • #13
Do you mean that matter particles do not degenerate at ground state?
 
  • #14
I do not know about QM saying of this things.So if we say not being degenerate,then I think we need a demonstration.
 
  • #15
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?
 
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  • #16
Conductor electrons in crystal have conserved momentum!
 
  • #17
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.
 
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  • #18
But there are many symmetries in crystal,so I think there are many observations that commute with Hamintonian(?)
 
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  • #19
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.
 

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