Does the third law of thermodynamics only constrain quadratic terms of the Hamiltonian?

[floyd0117]

The third law of quantum mechanics states that a system at absolute zero temperature has zero entropy. Entropy can be conceived as an expression of the number of possible microstates that can produce an identical macrostate. At zero entropy, there should be exactly *one* microstate configuration that can produce the macrostate in question.

For instance, take the following macrostate as an example,

- T = 0
- V = v, dV/dt = 0
- P = p, dP/dt = 0

Indeed the microstate describing this macrostate is unique in quadratic terms (the momentum of every particle must be zero). But it does not seem to be unique in the first-order terms - I can shuffle the positions of the particles all I want and keep producing the same macrostate.

So, by formal definition, is entropy only affected by quadratic and higher order terms of the Hamiltonian of the N particles contributing to the macrostate?

 

[Dale]

I can shuffle the positions of the particles all I want and keep producing the same macrostate.

Quantum particles are indistinguishable, so shuffling positions gives the same microstate.

 

[floyd0117]

Quantum particles are indistinguishable, so shuffling positions gives the same microstate.

Okay sure, I should have said to actually change the positions rather than "shuffling" them, so that each position is new and was not realized in the previous configuration.

Edit: could it be that there is in fact only one stable solution to the spatial configuration of a set of particles at T=0? And therefore I cannot change the positions and actually maintain absolute zero temperature?