Relationship between Enthalpy Fluctuation and Nonexponential Relaxation in Glass-forming Liquids

Abstract

A relationship between the equilibrium fictive temperature fluctuation σ(Tfe ) and the nonexponentiality βKWW is derived by extending the Adam-Gibbs equation within the Donth fluctuation-dissipation theorem to introduce a quantitative account for dynamic heterogeneity of supercooled liquids. The framework is validated against three structurally, chemically, and kinetically distinct glass-forming systems, namely B_2 O_3, Pd_43 Cu_27 Ni_10 P_20, and PVAc, without any adjustable fitting parameters. A condition for time-temperature superposition (TTS) is further derived as a balance between the fictive temperature fluctuation rate and a thermodynamic scaling term composed of the configurational entropy and heat capacity difference between glass and liquid. The present framework reveals the interplay between thermodynamic quantities, enthalpy fluctuations, and dynamic heterogeneity in glass-forming liquids.