What was Nakamura thinking with 62...g5 against Carlsen in Senquefield Cup 2018 rd. 9? I (a 2300 player) would never consider 62...g5 in this position giving White a protected passed pawn.  Nakamura either thought it was a drawing method, or the toughest defense, but Carlsen showed there is a clear winning plan for White. 62...g5 strikes me as a clear mistake but are other moves easier for White to win against?

I am trying to understand this decision by a 2800 player, thanks.
Let's say that Naka doesn't push g5 and instead waits (with for instance Rb7). Then it is white who can play g5+, taking advantage of the pin on the 6th rank. If black plays Kg6, then Kg4 and h5+ is unstoppable. It is clear that white is making progress. If black instead plays Kh5, then gxf6 hxf6, Rxf6 and black has lost a pawn and his king is completely stuck in a box. Rf5+ might be a possibility (taking on e5), black still cannot move the a pawn (due to an immediate Ra6 getting behind it), and again white has clearly made progress.

I believe Naka was sure that these lines were easy wins for white. Better to make the committal, but potentially holdable, g5 move, and try and hold the position with a static pawn structure, than sit and wait only to lose in a few moves.