What this page shows (at a glance)
- Start from a simple energy tally, convert to a dimensionless contrast e.
- Assign bounded, symmetric alignments for reactants/products.
- Compute a guarded, bounded RSI for a balanced reaction.
- Keep everything collapse-safe and plain ASCII.
Walkthrough (narrative)
We use one single-step reaction with declared scales. First, we form the contrast
from energies formed minus energies broken, scaled by the study’s Unit. Next, we map
that contrast to alignments with the symmetric tanh rule (reactants get the negative,
products the positive). Finally, we pool rapidities with stoichiometric weights and apply
an outer tanh to get RSI. Direction follows the sign of e; magnitudes stay bounded.
Plain ASCII formulas (copy-ready)
Inputs (single step)
E_broken = 300
E_formed = 420
E_unit = 100
c = 0.5
Contrast
e = (E_formed - E_broken) / E_unit
= (420 - 300) / 100
= 1.20
Alignment assignment (symmetric, bounded)
a_react = tanh(-c * e) = tanh(-0.5 * 1.20) = tanh(-0.60) ~ -0.5370
a_prod = tanh(+c * e) = tanh(+0.60) ~ +0.5370
Optional numeric RSI (default stoichiometry example)
# Example balanced skeleton: A + B -> C
# |m| = 1, gamma = 1 => W_r = 2, W_p = 1
U_r = sum w_r * atanh(a_react) = 2 * (-0.60) = -1.20
V_p = sum w_p * atanh(a_prod) = 1 * (+0.60) = +0.60
W_r = 2
s = (V_p - U_r) / W_r = (0.60 - (-1.20)) / 2 = 1.80 / 2 = 0.90
RSI = tanh(s) ~ tanh(0.90) ~ 0.7163 # products preferred
Notes
• Direction is positive (products favored) for any fixed stoichiometry, because e > 0 implies RSI > 0.
• Clamp any computed a to |a| <= 1 - eps_a (e.g., eps_a = 1e-12) before atanh(a) to avoid hitting +/-1.
• Use W_r_safe = max(W_r, eps_w) in code to guard division; here W_r > 0 so the guard is inactive.
Navigation
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