def
definition
def or abbrev
kl_divergence
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formal statement (Lean)
197noncomputable def kl_divergence {Ω : Type*} [Fintype Ω] (q p : Ω → ℝ) : ℝ :=
proof body
Definition body.
198 ∑ ω, if q ω > 0 ∧ p ω > 0 then q ω * log (q ω / p ω) else 0
199
200/-- KL divergence is non-negative (Gibbs' inequality).
201 D_KL(q || p) ≥ 0 with equality iff q = p. -/
used by (18)
-
coarse_graining_decreases_free_energy -
data_processing_inequality -
h_theorem_recognition -
EntropyAncestorCertificate -
free_energy_gap_is_kl -
free_energy_kl_identity -
gibbs_minimizes_free_energy_basic -
gibbs_unique_minimizer -
kl_divergence_zero_iff_eq -
kl_divergence_nonneg -
fe_kl_id -
free_energy_step_le -
JDescentOperator -
kl_divergence_antitone -
kl_le_of_le -
kl_step_le -
second_law -
SecondLawCert