<p>Lens DO concentrate light. That's their primary function. That's why you can burn ants with magnifiers. Given that you screen the _same_ image (not a bigger or smaller one) to a bigger and a smaller area, that area will receive the same amount of light. That's why you see the image coming from a projector lighter when you put the screen closer.<br /><br />Now, obviously, this is a bit of a hypothetical statement, as for the same lens you can't simply change the focal length keeping the view angle, so you can't screen the same image to a different sensor (maybe with an adapter). But for the sake of the main question, namely that how much sensor size matters in light gathering capacity in general - well, not too much. Apart from the fact that the sensor logic has a more-or-less fixed cost in space, and apart from another factor, namely that you can use wider apertures for bigger sensors, it doesn't matter at all.<br>
Sensors receive what comes from the lens (and the aperture), so the only thing what matters is how much light comes through them - which is a function of the size of the lens' outer area, the view angle (how much of the rays are relevant) and the aperture of course.<br>
This is the reason why you see tests on youtube claiming that the Sony a7r ii in crop mode has roughly the same low light capability as the Sony a7s ii.<br>
<em>"The total "amount" of light hitting the sensor is a function of the brightness of the image coming through the lens times the surface area of the sensor."</em><br>
This is just not true.</p>