Why this page. A clean, table-light way to reuse DeltaG, K, or Q to form the contrast e_G, then assign symmetric, bounded alignments without changing the RSI engine.
Meta description. Shunyaya Symbolic Mathematical Chemistry: turn DeltaG, K, or Q into a dimensionless e_G and bounded alignments; direction follows thermodynamics while G_unit and c adjust magnitude only.
Definitions (ASCII)
• Standard-state Gibbs free energy change: DeltaG_std (energy/mol)
• Nonstandard Gibbs (optional): DeltaG = DeltaG_std + R * T * ln(Q)
• Equilibrium link (optional): DeltaG_std = – R * T * ln(K)
• Gibbs contrast scale (declare once): G_unit > 0
• Study slope: c > 0 (as in §4.2)
• Gas constant: R = 8.314462618 J/(mol*K); temperature T in K
Contrast (replace e only; rest unchanged)
• Standard-state lens: e_G = ( -DeltaG_std ) / G_unit
• Nonstandard composition: e_G = ( -DeltaG ) / G_unit = ( -DeltaG_std – R * T * ln(Q) ) / G_unit
• If only K at T is known: e_G = ( R * T * ln(K) ) / G_unit
Alignment assignment (symmetric, bounded)
• a_r = tanh( -c * e_G )
• a_p = tanh( +c * e_G )
Then clamp so |a| <= 1 – eps_a using the same clamp policy.
RSI skeleton (unchanged, guarded)
• U_r = sum_r |m_r|^gamma * atanh_safe( a_r , eps_a )
• V_p = sum_p |m_p|^gamma * atanh_safe( a_p , eps_a )
• W_r = sum_r |m_r|^gamma ; W_r_safe = max( W_r , eps_w )
• RSI_G = tanh( ( V_p – U_r ) / W_r_safe )
Condition-aware use (optional)
• RSI_env_G = g_t * RSI_G # unified calm gate (see §5)
Minimal algorithm (per reaction, fixed T)
INPUT: {reactants}, {products}; gamma; G_unit; c; eps_a; eps_w; (optionally DeltaG_std or K or Q, T)
STEP 1: choose data path
A) have DeltaG_std -> e_G = ( -DeltaG_std ) / G_unit
B) have K, T -> e_G = ( R * T * ln(K) ) / G_unit
C) have DeltaG_std, Q, T -> e_G = ( -DeltaG_std – R * T * ln(Q) ) / G_unit
STEP 2: a_r = tanh( -c * e_G ); a_p = tanh( +c * e_G ); then
a_r = clamp_a( a_r , eps_a )
a_p = clamp_a( a_p , eps_a )
STEP 3:
U_r = sum_r |m_r|^gamma * atanh_safe( a_r , eps_a )
V_p = sum_p |m_p|^gamma * atanh_safe( a_p , eps_a )
W_r = sum_r |m_r|^gamma
W_r_safe = max( W_r , eps_w )
STEP 4: RSI_G = tanh( ( V_p – U_r ) / W_r_safe )
OPTIONAL STEP 5: RSI_env_G = g_t * RSI_G
OUTPUT: RSI_G in ( -1 , +1 ); sign( RSI_G ) = sign( e_G )
Sign sanity (why direction is preserved)
• If DeltaG_std < 0 (forward favored), then e_G > 0 ⇒ RSI_G > 0.
• If DeltaG_std > 0, then e_G < 0 ⇒ RSI_G < 0.
• If DeltaG_std = 0, then e_G = 0 ⇒ RSI_G = 0.
Guards and policy
• Units: keep R, T, DeltaG, G_unit consistent (all energy/mol). Do not mix J/mol and kJ/mol without converting.
• Scale: choose G_unit near a typical |DeltaG| for your study (see §4.4A); expose it in the manifest.
• Monotonicity: c > 0 preserves “more negative DeltaG ⇒ larger e_G ⇒ larger RSI_G”.
• Idempotence: if no thermo data, skip this bridge and use e from §4.1.
• Safety: observation-only; no rates or hazards implied.
Manifest additions (diffs from §4.12)
• G_unit # positive Gibbs scale (energy/mol)
• use_Gibbs # boolean flag: when true, set e := e_G
• data_path # one of {“DeltaG_std”, “K_T”, “DeltaG_std_Q_T”}
• R, T # constants if using K or Q (publish values)
Result. The thermo bridge swaps in a Gibbs-derived contrast e_G while keeping the same bounded alignment map and RSI engine. Directionality follows classical thermodynamics (sign of DeltaG), magnitudes remain tunable and transparent via G_unit and c, and collapse to classical stoichiometry is unchanged.
Navigation
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