First, I love both mages and anti-mages. Anti-mages are rather difficult to balance, as they are designed to hardcounter a good chunk of a team, and yet this tends to leave them completely vulnerable to the rest of the team. In general I don't think Riot does a good job of balancing them because they either end up overpowered compared to everyone (Veigar), or useless (LB, Kass). I will do my best to help you design the first working anti-mage, but I don't have any go to sources to point you at for balance.
Another thing to think about is that a lot of people are running bruisers mid as anti mages, because they're tankier than mages, have better burst, and can generally escape skill shots easily. They also can't be countered by traditional anti-mages. I haven't started looking over your abilities yet, but you might want to make sure you've covered AD casters in your anti-mage champ as well.
Stats: Would you mind including "at level 18" values? It cuts back on the amount of work reviewers have to do.
Passive: Entropy; I wouldn't add the slow component to true damage; people have to be able to mitigate the ability somehow. Chaotic Charge: Been seeing a lot of pasives like this recently, not sure why.
General Comment on Passive: Neither ability is really an anti-mage ability. An anti-mage is supposed to be better than a typical AP mid; usually this is either in the form of extra sustain (Veigar/Morg), or through escape mechanisms (LeBlanc, Kass). I think your Chaotic Charge ability proced a spell shield or something.
Q: Cd is low considering the effect persists for 5 seconds. I'd start it off around 18 seconds. It's an interesting cc ability, and I like it.
W: I don't see how this is helpful except maybe as a passive, in which case it already exists. Also, what if one person kills both clones?
E: Mana burn abilities are tricky creatures. I think Riot hasn't implemented any because they aren't fun (no skill involved, no counterplay opportunities). I'd probably rework this into something more like the q; either as a static AoE within which spells cost more than they normally would, or make it a consumable mark which will apply a similar debuff for a few seconds. If you go w/ the mark, you can have it so that the debuff applies as long as the mark is up, or is silenced (ending the extra mana consumed debuff) when the mark is consumed. I also don't think this ability would be particularly effective against energy champs as it is now.
R: I think the mechanism for this would be too glitchy, you'd have people bouncing back and forth at the border of the cc effect. I like innovation, but I think you'd be better off going with a traditional fear/terrify instead. Is the listed damage the damage per second (which would be way too much), or the damage total (could use a small buff)?