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An important extensive property of all systems in thermodynamics, statistical mechanics, and information theory, quantifying their disorder (randomness), i.e., our lack of information about them. It characterizes the degree to which the energy of the system is *not* available to do useful work.

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Why was the universe in an extraordinarily low-entropy state right after the big bang?

Entropy is poorly defined in most discussions. Entropy is not the increase in "disorder", nor is it simply the spreading out of energy. … With gravity, being spread evenly is difficult/rare and therefore low-entropy, and being clumped is easy/common and therefore high-entropy. …
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