On my OS X 10.9.5 system I'm seeing Dropbox consume CPU whenever anything on the file system changes, regardless of whether the changed files or folders are in the Dropbox synced folders. The CPU usage is proportionate to the rate of file system changes.
When I'm running an installer that takes a long time and has high disk activity (e.g. installing a documenation update in XCode), then the Dropbox CPU usage goes through the roof and I see the Dropbox sync status change from 'up to date' to 'indexing'. For less sustained activities with less intensive file system changes, I see Dropbox just popup briefly in the list of top CPU consumers -- but it shouldn't be showing up at all (or certainly not at double digit CPU use and not for the duration of the file system activity.
My guess is that Dropbox is simply listening for file system events and reacting to each one as if it might be change in a synced file or folder. It should be ignoring fsevents that are for items outside the Dropbox folders -- but it seems not to be the case. :-( :-(
I'm on 3.0.3, but have been seeing this problem since the 2.* days.
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Dave Hein