The central idea of "The Lord of Flies" is about what happens when you throw a group of adolescents together with no adult supervision. Let's be clear from the start. The book is a work of fiction, so the descent into a violent dictatorship is Golding's opinion. No such descent occurs in "Peter Pan," and that is also about a group of adolescents on an island free of adults.
Golding's central idea does match up with the scientific concept of entropy. Entropy says that everything moves from a state or order to a state of disorder. That's basically what happens on the island. The boys begin by trying to set order.
"Seems to me we ought to have a chief to decide things."
The boys recognize the need for leadership, hold a vote, and elect Ralph. Ralph then does what most leaders do. He delegates jobs to other boys.
"Jack's in charge of the choir. They can be--what do you want them to be?"
A symbol of that organized government system is the conch shell. It gives the boys a signal to come together for meetings, and acts as a tool to select who will be talking. When the conch shell is destroyed, all hope of the previous order is destroyed with it.
There was no chance of rescuing them and building up an outlaw tribe at the other end of the island. Samneric were savages like the rest; Piggy was dead, and the conch smashed to powder.
To Golding, the resulting savagery of the boys was always going to happen, because it's human nature. Humans can make attempts to avoid such behavior, but it's difficult and counter to human nature.