One question on average thermal velocity of free electron in metals

[ray.deng83]

Hi, I'm a student learning Solid State Physics and in a chapter of Classical Free Electron Theory of Metals in the textbook, it mentions "Since in the absence of a (electric) field there can be no net current, it is clear that the average thermal velocity over the equilibrium (thermal velocity) distribution must be zero." I don't quite understand why it should be zero. Can someone explain this to me?

 

[f95toli]

Because if it was not zero charges could accumulate in some part of the metal, which would violate the laws of thermodynamics (and it would also not be a equilibrium state anymore).

All that statement means is that electrons in a thermal equilibrium are -on average- not going anywhere.