Magnetic Moment of a system In thermal equilibrium 
"for a strictly classical system in thermal equilibrium can display no magnetic moment, even in a
magnetic field."

The statement is from Introduction to solid-state physics by Kittel (8th edition -Chapter 11), Why a system in thermal equilibrium can't have a magnetic moment? can anyone please give me more insight into this statement.
 A: Well, the full quote is:

Magnetism is inseparable from quantum mechanics, for a strictly classical system in thermal equilibrium can display no magnetic moment, even in a magnetic field.

More specifically, in thermal equilibrium + classical statistical physics the particles are Boltzmann distributed in energy $E$ according to: $$f(E) \propto \mathrm{e}^{-\frac{E}{k_{\mathrm{B}T}}},$$
where the key thing is that the total energy is the same function with or without a magnetic field $\mathbf{B}$. This is because the Lorentz force is $\mathbf{F}\propto q \mathbf{v}\times\mathbf{B}$ and hence $\mathbf{B}$ can do no work on the charge, adding to their energy $E$.
So basically the energy distribution is the same before and after the application of an external field. The system does not care. You'd expect an interaction energy $\propto \boldsymbol{\mu}\cdot \mathbf{B}$ where $\boldsymbol{\mu}$ is the magnetic moment. But since we've shown that this energy is $0$ even when $\mathbf{B} \neq 0$, you need to have $\boldsymbol{\mu} =0$. Here $\boldsymbol{\mu}$ is the net moment of the whole material. The macroscopic effect.
Now, microscopsically the electrons' orbits will be "bent" by the external field, as per the Lorentz force (ignoring quantum mechanics & the Schrödinger equation). There will even be induced currents when the field is switched on. But you are in thermal equilibrium, maximum entropy, so random distribution of currents because of the collisions needed to re-establish equilibrium. The net sum is zero.
On the contrary, in quantum mechanics there is an additional diamagnetic "screening current" that counteracts this. This is what eventually gives rise to a net $\boldsymbol{\mu}$.
A posteriori, you know that the magnetic moment of an atom/electron goes as the Bohr magneton $\mu_{\mathrm{B}}$ and hence as $\hbar$. The classical limit corresponds to $\hbar \rightarrow 0$, giving you no net magnetic moment.
