Nanoscopic heterogeneities in the thermal and dynamic properties of supercooled liquids

The theory of small system thermodynamics is applied to the Ising model plus kinetic energy, yielding a partition function for supercooled liquids. Several features near the glass temperature can be attributed to the resulting nanothermodynamic transition. A mean-field-like equilibrium energy exhibits Curie-Weiss-like behavior that provides an explanation for the Vogel-Tamman-Fulcher (VTF) law. Because this energy reduction is intensive, essentially independent of system size, the basic thermodynamic unit (called aggregate) subdivides into smaller regions (called clusters) lowering the net internal energy. The intensive energy reduction also yields relaxation rates that vary exponentially with inverse size, which when combined with the distribution of aggregate sizes provides an explanation for the Kohlrausch-Williams-Watts (KWW) law. Standard fluctuation theory gives a quantitative connection between the spectrum of response and the measured specific heat. Characteristic length scales from the model are related to direct measurements.