Glass-F eeze Analysis P o ocol: CPA + Cons ain Ra e
Compa ison
Deb a S. Ga an
No embe 2025
Abs ac
We es ed he CPA + Cons ain o mula ion o Dynamic P esen Theo y (DPΦ) agains
canonical o ho- e phenyl (OTP) iscosi y da a om Laughlin and Uhlmann (1972). The CPA
+ Cons ain model ep oduces he Vogel–Fulche –Tammann (VFT) e e ence wi h s a is ical
pa i y (R2= 0.9967 o bo h) and nea ly iden ical oo -mean-squa e e o (RMSE ≈0.235).
Despi e using one ewe empi ical cons an , he Con inuous P esen Ac ualiza ion (CPA) o -
mula ion g ounds he same cu a u e in physically mo i a ed cons ain dynamics a he han
cu e i ing. Unlike he VFT, he CPA + Cons ain o mula ion de i es his cu a u e om
i s -p inciples kine ics, linking iscosi y g ow h o cons ain -induced con inuous ac ualiza ion.
The esul s con i m nume ical equi alence and physical in e p e abili y o he new law.
1 Me hods
The iscosi y– empe a u e da a o o ho- e phenyl (OTP, 240–385 K) we e i ed using ou mod-
els: A henius, Vogel–Fulche –Tammann (VFT), CPA F eeze, and CPA + Cons ain . Nonlinea
leas -squa es op imiza ion (Le enbe g–Ma qua d ) minimized he RMS e o in log10(η). Model
selec ion employed AIC and BIC; 95% con idence in e als we e de i ed om he pa ame e co-
a iance ma ix.
Analysis was pe o med using GUI CPA F eeze Glass Be a (C. E. P ecke , 2025), used wi h
pe mission. Fi s we e execu ed on he canonical OTP iscosi y da ase o Laughlin and Uhlmann
(1972)[2]; esiduals and pa ame e s we e expo ed di ec ly om he GUI. All pos -p ocessing,
including igu e layou , compa ison able assembly, and esidual inspec ion, was pe o med by D.S.
Ga an .
The heo e ical basis o he CPA + Cons ain o mula ion is de ailed in Ga an and P ecke
(in p epa a ion, a Xi ).
2 Resul s
The CPA + Cons ain o mula ion ep oduces he Vogel–Fulche –Tammann (VFT) i o o ho-
e phenyl iscosi y (240–385 K) wi h s a is ical pa i y (R2= 0.9967, RMSE ≈0.235). Residuals
showed no sys ema ic cu a u e, and bo h models yielded indis inguishable accu acy ac oss he
empe a u e ange.
These esul s con i m ha he CPA + Cons ain model a ains he same quan i a i e pe o -
mance as he VFT while using one ewe empi ical cons an .
1
Figu e 1: Residuals o VFT and CPA + Cons ain i s.
Table 1: Fi me ics o o ho- e phenyl iscosi y models (240–385 K).
Model RMSE MAE Bias MAD R2AIC
VFT 0.2346 0.1989 −1.8×10−11 0.1770 0.9967 −95.50
CPA + Cons ain 0.2346 0.1989 −1.7×10−70.1770 0.9967 −91.50
CPA F eeze 1.6053 1.2747 0.0357 0.8978 0.8447 39.13
A henius 2.289 1.9479 −0.2821 0.5397 0.6843 61.97
3 Discussion
The CPA + Cons ain model ep oduces he empi ical VFT cu a u e wi h negligible s a is ical
di e ence while p o iding a mechanis ic in e p e a ion: iscosi y g ow h a ises om inc easing
cons ain densi y as he sys em app oaches i s cohe ence- eeze limi .
The obse ed pa i y sugges s ha he cu a u e adi ionally a ibu ed o empi ical i ing
e lec s eedback be ween con igu a ional cons ain and ac ualiza ion a e: beha io in insic o
Con inuous P esen Ac ualiza ion (CPA).
These indings alida e he CPA amewo k o Dynamic P esen Theo y (DPΦ) [1] as a physi-
cally mo i a ed eplacemen o pu ely empi ical iscosi y laws.
2
Da a and Code
Residual and pa ame e expo s, along wi h ep oduced esidual plo s, a e included in his eco d.
The analysis ool GUI CPA F eeze Glass Be a (C. E. P ecke , 2025) is a chi ed by i s au ho and
a ailable upon eques .
Acknowledgmen s
The au ho hanks C. E. P ecke o de eloping he CPA + Cons ain i ing ool and o his
assis ance in ep oducing he analysis. Compu a ional and analy ical suppo we e p o ided by
OpenAI GPT-5 and Google Gemini.
License and Ci a ion
Licensed unde CC-BY-4.0. Ci e as: D.S. Ga an (2025). Glass-F eeze Analysis P o ocol: CPA +
Cons ain Ra e Compa ison. Zenodo. DOI: 10.5281/zenodo.17546735.
Re e ences
[1] W. T. Laughlin and D. R. Uhlmann, J. Phys. Chem. 76 (14), 2317 (1972).
[2] D. S. Ga an , Dynamic P esen Theo y I: Uni ying Quan um Mechanics and Gene al Rela i i y,
Zenodo, DOI: 10.5281/zenodo.17069890 (2025).
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