Following a brief review of power-law distributions in nature, I shall explain why such observations pose a challenge for statistical physics, and the paradigm of self-organized criticality (SOC), introduced by Per Bak and coworkers [1]. SOC shows how scale-free event distributions can arise in the apparent absence of tuning parameters, in a system of many interacting entities, each having a threshold for relaxation, under a slow external drive. A similar mechanism has been suggested to underly power-law distributions of rain and drought [2]. SOC in its most familiar context, the "sandpile" models, is connected with a phase transition to an absorbing state [3]. I shall also discuss the generation of apparent power-law distributions via chaotic advection [4].
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