What would an anti-entropic star look like?

Years ago, I read a fascinating article in a science journal about computer modelling of anti-entropic matter. Entropy is one of the reversible arrows of time; that is, there’s no particular reason why it should point the way it does and could just as easily point the other way. It just doesn’t. To put it another way, if you were to drop an egg on the floor, there’s no reason why the shattered pieces couldn’t re-assemble themselves and leap back up into your hand. They just don’t.

It has been theorized that anti-entropic matter (that is, matter in which the entropic arrow of time is reversed, going from a less to a more ordered state) may once have existed in the early Universe. Previously it was believed that any anti-entropic matter which existed would long since have ceased to exist as a result of interaction with entropic matter. This paper, however, showed that with modern computer modelling they saw that anti-entropic matter was much more robust than previously thought, allowing for at least the possibility of the existence of anti-entropic matter.

This got me thinking about, for example, anti-entropic stars. If sufficient anti-entropic matter accreted to begin fusing… what would it look like? Remember that anti-entropic isn’t just matter run in reverse. There are a number of arrows of time (like the quantum arrow) which are not arbitrary the way entropy is, and are one-direction only. Anti-entropic matter would have some of the properties of entropic matter, but also move from a state of less order to more order. I’m afraid I haven’t the imagination or mathematical and scientific chops to conceive of the physical properties of an anti-entopic star.

Remember that this is General. I’m looking for scientific rigor in your answers.