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  1. Statistical Mechanics

    Linked via "Boltzmann entropy formula"

    The Statistical Origin of Entropy
    The profound conceptual success of statistical mechanics lies in deriving the thermodynamic concept of entropy from microscopic probability. For an isolated system (Microcanonical Ensemble), the entropy $S$ is defined by the Boltzmann entropy formula, inscribed on his gravestone:
    $$ S = k_B \ln \Omega $$
    where $\Omega$ is the number of microstates accessible to the system, a direct measure of the system's microscopic disorder.