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Johndcook

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Uniformity increases entropy

  • Entropy in a system is maximized when all possible states are equally likely.
  • Conversely, entropy is minimized when one outcome is certain to occur.
  • Moving towards uniformity increases entropy, while moving away from uniformity decreases entropy.
  • Entropy of a system with probabilities pi is defined by a specific formula.
  • If one probability is 1 and the rest are 0, entropy is 0.
  • When all probabilities are equal (pi = 1/n), entropy is log2(n), which is the maximum entropy.
  • The entropy function is concave, leading to entropy decreasing as movements away from uniformity occur.
  • Approaching the global maximum entropy of equal state probabilities results in monotonic entropy increase.

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