You can set this up with superconductors so they have zero resistance, but any wire will still have a trace inductance. (Moving charges must create a magnetic f

You can set this up with superconductors so they have zero resistance, but any wire will still have a trace inductance. (Moving charges must create a magnetic field, so if you're moving charges from one capacitor to another, you need to have some inductance somewhere). Once you include that, you'll see your LC resonator is perfectly undamped and oscillates the charges back and forth forever, breaking the assumption that a "steady state" would equalize the charge on both capacitors. The equations will also reveal the problem to you when you try to calculate the current that flows from one capacitor to another, with no inductance or resistance in between. You might try putting in an inductor and looking at the circuit behaviour in the limit as the inductance goes to zero -- you'd see the frequency of oscillation climbs to infinity; the full charge essentially teleports back and forth from one capacitor to the other, but still never settles into a steady state of equal charge on both capacitors. Once you see this, it's like having a problem set up with a frictionless ball on a hilltop beside a valley, saying "in the steady state, the ball has rolled down and settled in the valley. But there was no friction! Where did the energy go?", and the answer is just that the ball doesn't settle in the valley, but rather continues back up the other side, carried along by the kinetic energy that had been neglected in the problem statement. (Before the well-actualies point out that an LC circuit will damp itself via radiation, let's just say it's also perfectly shielded).