Axiomatic theories of ideal stretched exponential relaxation (SER)

Minimalist theories of complex systems are broadly of two kinds: mean-field (for example, hydrodynamic mode-coupling, random nucleation, lattice, or percolative fractal) and axiomatic. So far only axiomatic theories of properties absent from simple systems and intrinsic to complex systems, such as SER, have been quantitatively successful. SER is the prototypical complex temporal property of glasses, discovered by Kohlrausch 150 years ago, and now observed almost universally in microscopically homogeneous, complex non-equilibrium materials (strong and fragile network and fragile molecular glasses, polymers and copolymers, even electronic glasses). The Scher-Lax trap model (1973) is paradigmatic for electronic SER; for molecular SER Phillips (3IDMRCS 1995) identified two ‘magic’ shape fractions β = 3/5 and 3/7, as confirmed by many later experiments here reviewed. In the dielectric SER frequency domain involving ion conduction, there are also special beta values for fused salts and glasses, slightly, but distinguishably, different because of the presence of a forcing electric field.