wings of entropy and dual strike

I have looked everywhere and cannot find a definite answer.

How does wings of entropy work with dual strike?

Will it just deal its damage? or will dual strike count it as you having one in both hands?
(meaning main hand hits and off hand hits)

Also interested in how this works.

I use one and it seems like the physical for dual strike counts as one in each hand. so it double dips for the physical but not the elemental