IndisputableMonolith.Chemistry.ActivationEnergy
The ActivationEnergy module defines the J-cost function J(x) = ½(x + 1/x) - 1 and builds chemical activation barriers, Boltzmann factors, and Arrhenius rates from it in RS-native units. Researchers modeling reaction kinetics inside the Recognition Science framework cite these definitions when linking J-cost to transition-state stabilization. The module consists of direct definitions plus elementary nonnegativity and monotonicity statements.
claim$J(x) = ½(x + x^{-1}) - 1$. Activation barrier equals $J_transition - J_reactant$, Boltzmann factor is $exp(-activationBarrier)$, and Arrhenius rate is the temperature-dependent form built from these quantities.
background
The module resides in the Chemistry domain and imports the RS time quantum τ₀ = 1 tick from Constants. It introduces the J-cost function, which measures the recognition defect of a configuration x, together with reactant and transition-state specializations J_reactant and J_transition. ActivationBarrier is formed as their difference, after which boltzmannFactor and arrheniusRate are defined directly from it.
proof idea
This is a definition module. It states the J-cost formula, constructs the barrier and rate objects as immediate applications of J, and records the elementary facts barrier_nonneg, higher_barrier_slower, and higher_temp_faster.
why it matters in Recognition Science
These definitions supply the J-cost language required by the EnzymeCatalysis module, which treats enzymes as J-cost lenses that cancel the saddle at the transition state. The module thereby embeds classical activation-energy concepts inside the T5 J-uniqueness and RCL structure of Recognition Science.
scope and limits
- Does not compute numerical activation energies for concrete reactions.
- Does not treat multi-step mechanisms or solvent effects.
- Does not derive the Arrhenius form from microscopic dynamics.
- Does not incorporate pressure or concentration dependence.
used by (1)
depends on (1)
declarations in this module (22)
-
def
J -
def
J_reactant -
def
J_transition -
def
activationBarrier -
theorem
J_one -
theorem
J_nonneg -
theorem
barrier_nonneg -
def
boltzmannFactor -
def
arrheniusRate -
theorem
higher_barrier_slower -
theorem
higher_temp_faster -
def
E_coh -
def
barrierLadder -
theorem
hbond_barrier_scale -
theorem
covalent_barrier_higher -
def
catalyticFactor -
theorem
catalysis_lowers_barrier -
def
rateEnhancement -
theorem
enzyme_enhances_rate -
def
attemptFrequency -
def
eightTickPeriod -
theorem
attempt_freq_8tick