Can "up" here be dropped? What is the difference between "split" and "split up"?
"In this type of distribution, a client or server may be physically split up into logically equivalent parts, but each part is operating on its own share of the complete data set, thus balancing the load."
Distributed Systems, Tanenbaum
Yes, it's possible to leave out "up" after "split" in this particular sentence. However, it's better to leave it in the sentence.
"Up", in this example, and others, provides emphasis or greater clarification.
split them up - This means they're completely split. They are split in a noticeable and very obvious way. "Up" is a location, and "up" tells us that the splitting is in plain view and easy to see. This is, of course, an abstract view of splitting up.
The writer says "physically split up". However, this is still a rather abstract idea.
Here is "split up" in the physical sense of "splitting up".
The cabin owners split up the firewood among themselves. Everyone had enough for a campfire over the weekend.
Again, "up" signifies completion and that the splitting up is noticeable and in plain view. The splitting of, or the dividing of, the firewood is up where everyone can see it. Again, this is abstract. The only way to see the splitting up is to view the firewood in separate piles for each cabin owner. Then we can see that the firewood is, in fact, split up.
"Up" means something in "split up" or "divide up". If "up" didn't mean anything, then we could probably say "split down" or "split around". But we can't say either of those. And, in "split up", "up" goes with "split" for a reason. It's not just because someone felt like saying it. Each word has meaning.
In context, there's also an implied prepositional phrase.
They split the firewood up "into four piles".
And, of course, we notice that the same thing happens in your example sentence.