Is the vacuum a thermal state?

[naima]

Please look at the wikipedia article about thermal coherent states.
We can only consider the states centered at the origin ($\alpha$ = 0). If i understand what is written the vacuum is a pecular thermal state in the limit of a null temperature. I can understand that no energy can be borrowed from a system at this temperature. But this is because we used the word "temperature". How can we compute the energy that can be borrowed from a thermal coherent state? Is it N k T?
Thanks.

 

[Demystifier]

How can we compute the energy that can be borrowed from a thermal coherent state? Is it N k T?

It's NKT/2 when the Hamiltonian is quadratic in canonical coordinates and momenta. For more general Hamiltonians the relation is not so simple.