Nonlinear relaxation functions. Physical meaning of the Jonscher's power law

• The strongly nonlinear relaxation function is obtained.
• It is shown that the Jonscher's power law is the special case of obtained function.
• The physical meaning of both the obtained function and the power law is explained.

In this paper the strongly nonlinear relaxation function based on the vibrational model of relaxation polarization is obtained. The main properties of the obtained functions are described. We show that the obtained function is the special case of the nonlinear relaxation function (Lukichev, Chem. Phys., 428 (2014) 29); in turn, the Jonscher's power law is the special case of the strongly nonlinear function. The physical meaning of both the obtained function and the power law is explained by the vibrational model of relaxation polarization. The link between the shapes of the relaxation function tail and the left side slope of the corresponding loss peak is found.