How is the death on the island of Lord of the Flies different from the others, and what power and desire have become liberated in the children?Chapter 11
This is the first death on the island that results from intentional actions. Essentially, it's murder, not an accident. Other deaths, such as the boy's with the mulberry birthmark and Simon's, were either purely unintentional, or a result of a savage frenzy, rather than a pre-planned act. Yet Piggy's death is clearly calculated, motivated by evil and sadism:
The rock struck Piggy a glancing blow from chin to knee; the conch exploded into a thousand white fragments and ceased to exist. Piggy, saying nothing, with no time for even a grunt, traveled through the air sideways from the rock, turning over as he went. The rock bounded twice and was lost in the forest. Piggy fell forty feet on his back across that square red rock in the sea. His head opened and stuff came out and turned red. Piggy’s arms and legs twitched a bit, like a pig’s after it has been killed. Then the sea breathed again in a long, slow sigh, the water boiled white and pink over the rock; and when it went, sucking back again, the body of Piggy was gone.
As violent and shocking as Piggy's death is, Roger is described as having acted with "a delirious sense of abandonment". He is the evil incarnate, the one who takes pleasure in the pain and torture of others. His advancing on the twins, Samneric, at the end of the chapter represents that evil awakening on the island.
This is that "nameless authority", the power and desire that have, as you put it "become liberated in the children." The purposeful death of one has released the entire group from the bonds of society. They are now free to do whatever they please, whenever they please. After all, if one isn't punished for murder, what could possibly bring down punishment? Of course, with Jack in charge, anyone suspected of "treason" would be punished, to the delight of Roger.
This chapter encompasses events that mark the point of no return for the boys. Nothing will bring them back from their savagery until their rescue, and perhaps not even then.