It is said that charges inside a metal in electrostatic equilibrium are at rest, and are stationary. However, don’t the electrons have their own thermal vibrations and whatnot? Aren’t they always randomly moving? The sea of electrons isn’t immobile, is it? If there is no electric field within the conductor, then what is inducing these electrons to move about, changing direction at random (i.e. accelerate)? And is is then, true, that charges are really at rest in electrostatic equilibrium?
In the sea of electrons picture, the electrons in the conductor are not at rest: they are jiggling about like gas particles, colliding and changing direction constantly. You can think of them as billiard balls at zero gravity, confined in the volume of the piece of conductor at hand.
According to thermal physics, their average kinetic energy is related to the temperature of the metal and all this random movement contributes to the blackbody radiation of the metal.
But this is not in contradiction with electrostatic equilibrium.
Electrostatic equilibrium requires there be no currents. But the random movements of the vast number of electrons in all directions and speeds cancels out and there is no overall movement of charge: no current.