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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Fractional thermodynamics resolves the Stokes-Einstein breakdown in supercooled water.

Farrukh A Chishtie^1,2,3

¹Peaceful Society, Science and Innovation Foundation, Vancouver, BC, Canada. fachisht@uwo.ca.

Scientific Reports

|July 7, 2026

Summary

Supercooled water

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Area of Science:

Physical chemistry
Thermodynamics
Soft matter physics

Background:

The Stokes-Einstein relation describes particle diffusion in liquids.
This relation breaks down in supercooled water, a phenomenon lacking theoretical explanation.
Anomalous diffusion in hydrogen-bonded liquids remains a significant challenge.

Purpose of the Study:

To develop a theoretical framework explaining the breakdown of the Stokes-Einstein relation in supercooled water.
To quantitatively resolve the anomaly in the diffusion dynamics of supercooled water.
To establish the role of fractional calculus in understanding anomalous transport.

Main Methods:

Development of a two-state fractional thermodynamics framework.
Analysis of translational and rotational degrees of freedom using fractional dynamics.
Application of fractional Landau theory to derive critical exponents.

Main Results:

The developed framework quantitatively explains the breakdown of the Stokes-Einstein relation with 1.0% experimental agreement.
Identified distinct fractional dynamics for translational (approaching ballistic) and rotational (subdiffusive) motion.
The decoupling ratio, combined with percolative transport and critical fluctuations, resolves the anomaly.

Conclusions:

Fractional calculus is essential for understanding anomalous transport in hydrogen-bonded liquids.
The study provides a robust theoretical explanation for the breakdown of the Stokes-Einstein relation.
Testable predictions for neutron scattering and molecular dynamics simulations are presented.