Abstract
A theory for the nonlinear energy response to the oscillating tempearature is developed and the nonlinear ac specific heat is defined. The theory is applied to the glass forming model with the free energy landscape picture and the characteristics of the linear and nonlinear ac specific heats in the glass forming materials are shown: (1) The width of the imaginary part of the 1st order ac specific heat broaden and the frequency at the peak of the imaginary part shifts to the low frequency region as the temperature decreases below the glass transition point. (2) The nonlinear ac specific heat, which is defined from the nonlinear energy response to the oscillating temperature, shows the anomally at the glass transition point and diverges at the Vogel-Fulcher temperature in the glass forming model. This divergence behavior is similar to that of the nonlinear magnetic susceptibility of the spin glasses. In this paper, the free energy landscape picture is briefly introduced and the characteristics of the linear and nonlinear ac specific heats are explained.
https://ror.org/00p4k0j84 
