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I don't believe so. If a piece of content is popular, most of the time users continue to comment on it, like it, share it. The continued commentary itself keeps it at the top of streams. I would suspect that's the reason for the gap.
Perhaps as a back channel/manually intensive way of doing this is to leverage community manager reports (which give you info on popular content by view) and the featured content widget.
Popular content items, once established, can change very little. Also keep in mind that either a featured content or most view content widget will increase the amount this document is viewed. They continue to be popular because they are popular, rather than organic.