The damage increases proportionately, have confirmed it myself. The same goes for other DoT skills in the game that have their duration buffed by some passive or by leveling the skill.
As for how many ticks that adds, it's either 2 or 3.
It ticks once/second, so it un-doubtedly adds at least 2. But this is where it gets dicey... I believe ticks trigger at the beginning of the second like...
First tick @ 0.1 seconds after cast...
Second tick @ 1.1 seconds after cast...
And so on. If that's the case, than I'd expect the .4 second duration to trigger one last tick.
I have confirmed this to be the way that poisons work, such that if a poison has a say, 7.2 second duration, you'll actually see a total of 8 ticks. So it's reasonable to assume that other DoT-type effects will work the same.
The easiest way to confirm this is to use either an addon, or enable scrolling combat text and count the number of times you see the damage tick.

However, I do want to ask, in case I can help you avoid some sub-par build choices here... why are you interested in the damage of a skill like Entropy?
It's damage is horrible to be honest. It's almost entirely a buff skill, used for Major Sorcery, Empower procs, and mayyyybe the little passive of 5change to heal on light-heavies or the 5 max health bonus of the two morphs. It's damage is so low that it takes it an entire 14 seconds to deal that damage that even a mediocre skill can do in one hit/one second.
I really wouldn't worry about it's damage all that much.

@LinearParadox @Nestor

It would strictly be for enabling the use of trash mag pots (by providing major sorc, with major prophecy from magelight) on a new PvE magblade I intend to create, since I have a flex slot on the backbar to accomodate it.

I figured it'd be sub-optimal damage-wise, but I wanted to know how much by.

That said... seeing as it gets boosted by the passive, its tooltip would actually be higher than one cast of swallow soul, with further damage added thereafter due to the empower proc. And it synergises with Skoria, which I'll also be running. It could even slightly boost my DPS, possibly?

I finally removed Entropy from my bar, and improved the overall performance of my magblade. Sap Essence provides part of what you need if it will be a longer fight. For boss fights I go the direction of alchemy and use potions to gain Major Prophecy and Major Sorcery.

All of that being said I do think that Entropy is a good way to get the buff until you get Sap Essence or can raise up your alchemy passives.