Earlier quoted context omitted.
Well....1920x1080@3 bytes per pixel@60Hz = 336MB/s, while 3200x1800@3 bytes per pixel@60Hz = 989MB/s. In QHD mode your laptop is sending nearly a gigabyte of data to the display...per second. It might not be very power hungry to compute those pixels with a modern GPU, but even simply sending that much data requires a lot more power than sending "only" 330MB/s.
I'm not so sure. Given this random google hit (on 10gbps ethernet nics) -- I'm not sure it makes much difference: http://www.cl.cam.ac.uk/~acr31/pubs/sohan-10gbpower.pdf I couldn't find anything on hdmi/4k, but this seems to suggest it doesn't make much difference (compared to what I assume the backlight and screen draws): http://en.wikipedia.org/wiki/Thunderbolt_(interface) At any rate, if we assume it takes 4 times…
I could be wrong about how significant the backlight is on an LED display though.
I also thought that modern video cards (as in from the last 15-20 years) optimized 2D graphics so that regular desktop use didn't require pushing a screen full of pixels to the GPU on every frame. That would seem to diminish the significance of the actual number of pixels at QHD+.
I don't have a good answer.