Connecting the microcanonical with the (grand) canonical ensemble

In summary: This is an approximation that is valid for low interaction strengths, non-degeneracy, and no entanglement. Here's why:1. Interaction strength: In a strongly interacting gas, the atom's Hamiltonian will depend on parameters that are outside the single-atom system, and so you need to take the whole gas into account. In a weakly interacting gas, I believe you can get away with a mean-field solution, which will have its own Maxwellian statistics.2. Quantum degeneracy: If a gas is deeply degenerate, then you cannot distinguish one molecule from its neighbors, so it makes no sense to define a one-molecule system. Even if you could, you
  • #36
I don't know. I'd say, just post such an "intro posting" and see what happens.
 
  • Like
Likes Twigg and Philip Koeck
Science news on Phys.org
  • #37
vanhees71 said:
I don't know. I'd say, just post such an "intro posting" and see what happens.
It's started.
 
  • Like
Likes vanhees71
  • #38
Philip Koeck said:
Then I'll go a step further and decide that the system should consist of a single atom.
It doesn't matter whether the number of particles is ##N=1## or ##N=10^{23}##. One has to distinguish the number of particles in the system (which doesn't need to be large), from the number of systems in the ensemble (which must be large). In the Gibbs theory of ensembles, an ensemble is a fictitious ensemble; it's a thing we imagine to conceptualize the notion of probability. For example, you can say that the probability of a single coin to be in the heads state is 1/2, but to conceptualize this you can imagine that you flipped this single coin a 1000 times.

That being said, once you said that ##N## is fixed (##N=1## in your case), you can talk about a canonical ensemble, but not about a grand-canonical ensemble.
 
  • Like
Likes Philip Koeck and vanhees71

Similar threads

Back
Top