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Updated: Jul 9, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Fractional thermodynamics resolves the Stokes-Einstein breakdown in supercooled water
Farrukh A Chishtie1,2,3
1Peaceful Society, Science and Innovation Foundation, Vancouver, BC, Canada. fachisht@uwo.ca.
Scientific Reports
|July 7, 2026
Summary
Supercooled water
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.
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