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    • https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_III_(Chong)/06%3A_Appendices/6.03%3A_C-_Entropy
      Take x=1/(Wpi) where W is the number of microstates: \[\begin{align} \begin{aligned} \ln \left[\frac{1}{Wp_i}\right] &\le \frac{1}{Wp_i} - 1 \quad \textrm{for}\;\textrm{all}\; i = 1,\dots, ...Take x=1/(Wpi) where W is the number of microstates: ln[1Wpi]1Wpi1foralli=1,,W.Wi=1piln[1Wpi]Wi=1(1Wpi)Wi=1pilnWWi=1pilnpi11=0kbWi=1pilnpikblnW. Moreover, the equality holds if and only if \(p_…

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