def definition def or abbrev

`VFE`

No prose has been written for this declaration yet. The Lean source and graph data below render without it.

formal statement (Lean)

  53def VFE (q : ProbDist ι) (E : ι → ℝ) (β : ℝ) : ℝ :=

Definition body.

  54  ∑ i, q.prob i * E i + (1 / β) * ∑ i, q.prob i * Real.log (q.prob i)
  55
  56/-- The Boltzmann reference probability for `(E, β)`. -/

From the project-wide theorem graph. These declarations reference this one in their body.

boltzmann_minimizes_vfe in IndisputableMonolith.Statistics.VariationalFreeEnergyFromRCL decl_use
kl_nonneg in IndisputableMonolith.Statistics.VariationalFreeEnergyFromRCL decl_use
vfe_at_boltzmann_eq_helmholtzF in IndisputableMonolith.Statistics.VariationalFreeEnergyFromRCL decl_use
VFECert in IndisputableMonolith.Statistics.VariationalFreeEnergyFromRCL decl_use

Lean names referenced from this declaration's body.

prob in IndisputableMonolith.Decision.StPetersburg decl_use
probability in IndisputableMonolith.Foundation.QuantumLedger decl_use
E in IndisputableMonolith.Foundation.SpectralEmergence decl_use
for in IndisputableMonolith.Foundation.UniversalForcingSelfReference decl_use
ProbDist in IndisputableMonolith.Information.ShannonEntropy decl_use
probability in IndisputableMonolith.QFT.SMatrixUnitarity decl_use
ProbDist in IndisputableMonolith.Statistics.VariationalFreeEnergyFromRCL decl_use
probability in IndisputableMonolith.Thermodynamics.BoltzmannDistribution decl_use