Lol, how sure are we that Arsenal will finish second? Arsenal second position is under threat from Newcastle United and Manchester City. It's just five points and six points that separate the second, third and fourth team respectively while we still have four more games to round up the season. The fact that we all agreed Manchester City is extremely bad this season but they're still in the top four contesting for champions league slot tells how superior they are. Look at their Manchester united counterpart having a bad season and comfortably switching positions in the third quarter table.
I don't know about reducing the 5 points to Arsenal in the remaining 4 rounds, I don't think it's possible. Especially since Arsenal's opponents are not that strong and important, because there are games against Bournemouth and Southampton, Arsenal will most likely win these games.
There is another game with Liverpool, and Liverpool have already become champions, most likely they will not have the motivation for this game. And they will play with Newcastle, well, maybe they will lose it or even play a draw. In any case, it seems to me that second place will be secured for Arsenal, there is almost no doubt about it.