boltzmannFactor
This definition supplies the numerical value of Boltzmann's constant k_B in SI units to connect thermodynamic entropy S = k_B log W with Shannon entropy H for uniform distributions. Information theorists and chemists working inside the Recognition Science framework cite it when scaling J-cost measures to physical energies. The declaration is a direct constant assignment with no computation or lemmas.
claimLet $k_B$ denote Boltzmann's constant, defined by the value $1.38 times 10^{-23}$ J/K.
background
The Information.ShannonEntropy module derives Shannon entropy from J-cost over probability distributions. J-cost is given by J(x) = (x + x^{-1})/2 - 1 and quantifies recognition effort for each probability ratio; total J-cost minimization over a distribution recovers H = -sum p_i log p_i. The module doc-comment states that thermodynamic entropy connects via S = k_B log W = k_B times H for uniform cases. Upstream results supply functional Boltzmann factors exp(-E/kT) in chemistry and thermodynamics modules together with the dimensionless bridge K = phi^{1/2}.
proof idea
Direct constant definition that assigns the numerical value 1.38e-23. No lemmas or tactics are invoked; the declaration is a one-line noncomputable assignment.
why it matters in Recognition Science
The definition closes the link between the module's J-cost derivation of Shannon entropy and classical thermodynamics, as noted in the doc-comment. It is referenced by downstream chemistry results on activation energy and enzyme catalysis that apply Boltzmann factors to rates. Within the Recognition Science framework it supports the information-theoretic step that follows the phi-ladder and eight-tick octave, while leaving open the derivation of the numerical value itself from the J-uniqueness relation.
scope and limits
- Does not derive the numerical value from J-cost or phi-ladder axioms.
- Does not prove the entropy identification S = k_B H; that occurs in sibling theorems.
- Does not express k_B in RS-native units.
- Does not include temperature or energy scaling.
formal statement (Lean)
220noncomputable def boltzmannFactor : ℝ := 1.38e-23 -- J/K
proof body
Definition body.
221