Some remarkably universal empirical formulas are used to characterize the slow dynamics of disordered materials and imperfect crystals. Stretched-exponential relaxation is used for time-dependent response, non-classical critical scaling is used for temperature-dependent behavior, and 1/f noise is used for frequency-dependent fluctuations. I will describe a common physical foundation for all of these formulas. The behavior may be attributed to strict adherence to the laws of thermodynamics: energy is conserved using Hill’s subdivision potential for nonlinear terms, entropy is maximized using a local thermal bath, and similar states are treated using the statistics of indistinguishable particles. Alternatively, the mechanism may be interpreted using information theory for reversible fluctuations. I will emphasize how specific models based on these principles yield the empirical formulas, plus deviations from the formulas that often match the measured behavior.
