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1. Statistical Mechanics

   Linked via "Shannon entropy"

   where $\Omega$ is the number of microstates accessible to the system, a direct measure of the system's microscopic disorder.
   In the Canonical Ensemble, the relationship is generalized via the definition of the average Shannon entropy of the probability distribution $p_j$:
   $$ S = -kB \sum{j} pj \ln pj $$
   This generalization demonstrates that higher entropy corresponds to a broader, flatter probability distribution across the microstates.