That's simply a mathematical description of it. We're saying that antimatter moving forwards in time is mathematically identical to matter moving backwards. Matter can be thought of as antimatter moving backwards in time, too.
The 2nd law of thermodynamics (entropy increases) comes from the definition of entropy: high entropy means that there are lots of ways to arrange things microscopically so that they're indistinguishable at our level. That means necessarily that there are more high entropy states than low entropy states, so by pure probability evolving a system in time (in either direction) leads to a higher entropy system. It's got nothing to do with individual particles moving forwards or backwards in time.
Most of what you consider to be consequences of time moving forwards are consequences of entropy increasing: a being moving "backwards" in time isn't going to remember the future, because remembering is about being able to work backwards from your current high-entropy state to a low-entropy past. Imagine you have a photograph: if entropy was lower in the past, it probably resulted from the lower entropy situation of a camera photographing the subject. If it wasn't lower, then it might just be a random chance collection of atoms that used to be a high-entropy gas.
So to answer your question: antimatter is going to obey the same laws here as everything else. Entropy increases because we don't know anything about the future, and know that in the past it was lower. The same applies to antimatter.
Sorry for the wall of text - but if you're interested you should read this book, which does a remarkable job of explaining entropy.
Check out “From Eternity to Here”
https://www.amazon.com/Eternity-Here-Quest-Ultimate-Theory/dp/0452296544/ref=nodl_
I couldn't understand it either, until I read this:
https://www.amazon.ca/dp/0452296544/ref=cm_sw_r_cp_apa_i_6H2MFbW5197T8
I cannot recommend enough this book "From Eternity to Here", a book that explores time as a thermodynamic phenomenon.
First article: http://mobile.nytimes.com/2016/12/12/opinion/can-evolution-have-a-higher-purpose.html
There's a link in there to another article that is also good.
Here's a talk given at a Mormon transhumanist conference. It's not really tied to mormonism, especially not this talk.
The guy speaking is a friend of mine, and he describes himself as an agnostic, leaning toward the theist side. His definition of god is very different from the typical definition. It's more like the process of evolution heading towards more complexity and more cooperation, it is possible that there is something directing that. Of course there is no conclusive proof, there really cannot be, but it is still interesting to think about.
I also like a concept called the arrow of time. Here's a fun music video for an intro.
Look in the description for a link to the lecture that inspired the music video. The professor is Sean Carroll, and my friend recommends his book, https://www.amazon.com/Eternity-Here-Quest-Ultimate-Theory/dp/0452296544
I hope that helps!
You can take it wherever ya want, but take this map!
Have you seen Mr. Nobody?
I highly recommend it
But read this first:
https://www.amazon.com/Eternity-Here-Quest-Ultimate-Theory/dp/0452296544
We know many things, and many questions are still unanswered.
http://www.amazon.com/Eternity-Here-Quest-Ultimate-Theory/dp/0452296544/
If we exactly reversed all the velocities of the particles we would in fact see them becoming "un-mixed" and entropy would be going down. It would exactly look like running a recording played backwards. The point is that these particles are not set to random velocities and positions. They have a past of low entropy and their microstate is conditioned on this fact. This makes those positions and velocities extremely special when you look in that direction of time.
This is getting a little more controversial, but according to this I do have people like Einstein, Boltzmann and Feynman on my side. In the broader picture about time the distant past of the big bang, which had extremely low entropy. This is sort of a low entropy boundary every state in the universe is conditioned on. The 2nd law of thermodynamics would predict that entropy increases in both directions of time, was it not for that condition. It's called the past hypothesis.
Cosmologist Sean Carroll from caltech has a great book on the entire subject called From Eternity to Here: The Quest for the Ultimate Theory of Time.
And a bunch of youtube videos like Arrow of Time - Sixty Symbols.
http://www.amazon.com/From-Eternity-Here-Ultimate-Theory/dp/0452296544 is tough , but really interesting IMO.
Sean Carroll wrote a book about time too, where it's all about entropy. You can always check out the amazon page of a book for a summary. Here's Carroll's: http://www.amazon.com/From-Eternity-Here-Ultimate-Theory/dp/0452296544
I don't personally subscribe to either view, I think time is more fundamental than entropy and there's no good reason to believe our universe "closes up on itself".
Also here's a short Carroll talk on the subject of time: https://www.youtube.com/watch?v=WMaTyg8wR4Y#
I have read some Greene but I found Sean Carroll's "From Eternity to Here" much more illuminating in regards to the direction of time and entropy in general. http://www.amazon.com/From-Eternity-Here-Ultimate-Theory/dp/0452296544