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def definition def or abbrev

boltzmannDist

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  57def boltzmannDist (E : ι → ℝ) (β : ℝ) : ProbDist ι :=

proof body

Definition body.

  58{ prob := fun i => boltzmannProb E β i
  59  prob_pos := boltzmannProb_pos E β
  60  prob_sum := boltzmannProb_sum_one E β }
  61
  62/-! ## Gibbs inequality (KL nonnegativity)
  63
  64For two strictly positive distributions p, q on the same finite type with
  65sum 1, KL(p || q) := sum_i p_i log(p_i / q_i) >= 0, with equality iff p = q.
  66
  67We prove the inequality directly using `Real.log_le_sub_one_of_pos`. -/
  68

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