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This is an educated guess (i have never come across the analogy of an egg). Entropy is a measure of the disorder of a system. An egg shell contains the egg. When cracked, the egg is free to run out of the enclosed system, and it is unpredictable as to where the egg will go, thus it has become less ordered. It could also be less ordered as air can interact more freely with the egg, thus potentially spoiling it more freely than when it had its protective casing.

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