Non-Equilibrium Statistical Mechanics of Glass-Forming Liquids under Continuous Cooling: Microscopic Inner Clocks, Fictive Temperatures, and Kauzmann Diagrams
Abstract
The description of macroscopic properties in out-of-equilibrium amorphous solids such as gels and glasses, typically processed under finite cooling rates, remains a fundamental challenge for modern statistical physics. In this work, we employ the Non-Equilibrium Self-Consistent Generalized Langevin Equation (NESCGLE) theory to construct a microscopic description of the structural and calorimetric glass transition under continuous cooling. Building upon the microscopic Onsager-Machlup interpretation of Narayanaswamy's material time (the inner clock u(t)) [J.Chem.Phys. 156, 244506 (2022)], we recover Tool's fictive temperature Tf directly from the evolving spatial pair correlations and show that wavenumber dispersion naturally generalizes the classical scalar Tf into a continuous mode spectrum governed by de Gennes narrowing at the primary cage peak. Across wide variations in cooling rate down to the quasi-static limit, the theory yields first-principles non-equilibrium Kauzmann diagrams for the two-body excess entropy that dynamically avert the Kauzmann crisis above the ideal dynamic arrest temperature Tc, while predicting sigmoidal relaxational heat-capacity steps consistent with computer simulations and calorimetry. Finally, we extract the cooling-rate-dependent glass transition temperature Tg(q) from both equal-area integrals and differential heat-capacity landmarks, demonstrating that its asymptotic approach toward Tc obeys a critical power-law scaling governed directly by the equilibrium dynamic arrest exponent.
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BibTeX
@misc{peredoortiz2026nonequilibrium,
title = {{Non-Equilibrium Statistical Mechanics of Glass-Forming Liquids under Continuous Cooling: Microscopic Inner Clocks, Fictive Temperatures, and Kauzmann Diagrams}},
author = {R. Peredo-Ortiz and M. Medina-Noyola and L. F. Elizondo-Aguilera},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00382},
eprint = {2611.00382},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00382},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-Equilibrium Statistical Mechanics of Glass-Forming Liquids under Continuous Cooling: Microscopic Inner Clocks, Fictive Temperatures, and Kauzmann Diagrams
AU - R. Peredo-Ortiz
AU - M. Medina-Noyola
AU - L. F. Elizondo-Aguilera
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00382
UR - https://arxiv.org/abs/2611.00382
AB - The description of macroscopic properties in out-of-equilibrium amorphous solids such as gels and glasses, typically processed under finite cooling rates, remains a fundamental challenge for modern statistical physics. In this work, we employ the Non-Equilibrium Self-Consistent Generalized Langevin Equation (NESCGLE) theory to construct a microscopic description of the structural and calorimetric glass transition under continuous cooling. Building upon the microscopic Onsager-Machlup interpretation of Narayanaswamy's material time (the inner clock u(t)) [J.Chem.Phys. 156, 244506 (2022)], we recover Tool's fictive temperature T_f directly from the evolving spatial pair correlations and show that wavenumber dispersion naturally generalizes the classical scalar T_f into a continuous mode spectrum governed by de Gennes narrowing at the primary cage peak. Across wide variations in cooling rate down to the quasi-static limit, the theory yields first-principles non-equilibrium Kauzmann diagrams for the two-body excess entropy that dynamically avert the Kauzmann crisis above the ideal dynamic arrest temperature T_c, while predicting sigmoidal relaxational heat-capacity steps consistent with computer simulations and calorimetry. Finally, we extract the cooling-rate-dependent glass transition temperature T_g(q) from both equal-area integrals and differential heat-capacity landmarks, demonstrating that its asymptotic approach toward T_c obeys a critical power-law scaling governed directly by the equilibrium dynamic arrest exponent.
ER -