A model for nonexponential relaxation and aging in dissipative systems.

The nonexponential relaxation and aging inherent to complex dynamics manifested in a wide variety of dissipative systems are analyzed through a model of diffusion in phase space in the presence of a nonconservative force. The action of this force establishes a heat flow which maintains the system away from equilibrium. The inability of the system to find its equilibrium state becomes apparent through the presence of an effective temperature field. This is the temperature of the stationary nonequilibrium state reached by the system satisfying a generalized version of the fluctuation-dissipation theorem. The presence of a nonequilibrium temperature leads to a hierarchy of relaxation times responsible for the aging phenomena and to a relation similar to the Vogel-Fulcher-Tammann law [H. Vogel, Phys. Z. 22, 645 (1921); G. S. Fulcher, J. Am. Ceram. Soc. 8, 339 (1925); 8, 789 (1925); G. Tammann and W. Hesse, Z. Anorg. Allg. Chem. 156, 245 (1926)].