Well as long as you are using HDMI you won't be able to get better than 1080P Resolution.
Perhaps I'm wrong or you misunderstood me. That thunderbolt port is a dual port TB or MiniDP?
On Further looking around, HDMI is the best you can do unless your monitor has a Display Port or a Thunderbolt port. I think your refresh rate is Monitor dependent your GPU is capable of faster refresh rates. Its just that the screens on our NB's don't support faster refresh rates. That is unless you have a 3D configuration model then it will have a screen of lower resolution but 120 hz refresh rate
HDMI you'll get 1080P and digital sound. refresh rate should be monitor dependent
MiniDP/TB to Hdmi you get the same
MiniDP/TB to DVI you get higher resolution but no sound, as far as know DVI has never piped sound only Video.
mDP/TB to Display Port you should get Higher resolution and digital sound
A quick check on Amazon it looks like adapters are not created equal some will pass through higher resolutions than others. You should research this since you have either the mDP or TB and that should give you the best resolutions
Also looked up the model Monitor you called out it also has
Display Port and Native resolution 1920 1080 at least the one on Amazon does?
I may be wrong about your TB port also being a mDP, when we first got our G75VW there was a lot of misinformation about the mDP and TB I thought I remember somewhere in the original manual that there was a way to Switch between these. I can't seem to find that information now on how that switch would have been accomplished I do remember that is was software driven Perhaps a setting in the BIOS? However all that may have been some of the misleading advertising Asus was putting out about the G75VW back in 2012
All this is meaning less since the monitor in question is only 1080 monitor HDMI will fully support it. You would only need mDP or TB for a monitor that would support Higher resolutions
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