This is a good introduction to power law distributions.

Most natural events and outcomes follow Gaussian and Poisson distributions. They are made up of random, independent factors. But there are certain events which follow power-law distributions.

This is connected with phase transitions and critical points. When ice reaches a critical point it undergoes a phase transition to water. Likewise, the evaporation of water into gas. This is measured through the heat in the system. Self-organized Criticality is responsible for some, but not all, phase transitions. The Sand pile model most often used to illustrate the idea.

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