Polys are all but irrelevant.
Lighting is a pixel shader issue, and so does absolutely scale linearly with that.
Postprocess also does.
In modern games, the bottleneck is 99% of the time on the pixel shader. There's no real reason to go hod wild on polycounts when a 80k character with normal\AO maps looks just as fine as a 800k character.
The pixel shader handles all lighting and shadowing, which is what is really expensive.
Physics runs in it's own thread, and generally it's CPU, so it doesn't really matter. If physics is the bottleneck, a more powerful GPU isn't gonna help in most cases.
It's not exactly 4x, but for example on my UE4 game the bottleneck is the GPU, and it's roughly 2ms vertex shader, 9ms lighting&shadowing (Pixel shader), 3ms Postprocess.
4x resolution (1080 to 2160\4k) nets 34ms pixel shader, with vertex shader unchanged and postprocess in between that.
It's ~3-3.5x the compute power needed.