Changes — On Antibody Repertoires
2026-06-19 — Statistical-mechanics tutorial fused into the affinity-distribution section
- Added stand-alone in-depth page
writing/binding-statistical-mechanics.qmd (“From the Boltzmann distribution to receptor–ligand kinetics”): the full 13-section tutorial (Boltzmann distribution → Langmuir isotherm → kinetics → diffusive barrier crossing → affinity-distribution paradigm → effective temperature → competition/scarcity → REM freezing transition → Prechl super-landscape correspondence → interactive simulation → caveats), rewritten with undergraduate-friendly scaffolding and Quarto/MathJax math.
- Linked it bidirectionally from
writing/affinity-distribution.qmd (callout near the top + closing pointer); the essay remains the working-level summary, the new page the derivation.
- Embedded the competition × freezing animation
figures/binding_competition_freezing.gif (84-frame mass-conservation sweep, M=40, σ/kT = 0.6 vs 3.0) generated by figures/make_competition_freezing.py.
- Science review of the source tutorial: confirmed the sign convention (Δε < 0 favorable; K_D = l0·e^{+Δε/kT}), the K_D = k_off/k_on terminology fix, the diffusive (Kramers/Smoluchowski) correction to the “flying molecules” picture, the REM freezing law β_c = √(2 ln M)/σ and frozen-phase order parameter Y = 1 − T/T_c, and the Prechl correspondence ν_S = 1/ν_H − 1 with T_eff = ν_H·T (verified against arXiv:2306.04665).
- Added references: Prechl 2017 (F1000 fountain landscape), Kramers 1940, Smoluchowski 1917, Derrida–Gardner 1986 (GREM), Emberly SFU PHYS 347 notes.