A theory for the nonlinear energy response of a system subjected to a heat bath is developed when the temperature of the heat bath is modulated sinusoidally. The theory is applied to a model glass forming system, where the landscape is assumed to have 20 basins and transition rates between basins obey a power law distribution. It is shown that the statistics of eigenvalues of the transition rate matrix, the glass transition temperature T g , the Vogel-Fulcher temperature T 0 and the crossover temperature T x can be determined from the 1st-and 2nd-order ac specific heats, which are defined as coefficients of the 1st-and 2nd-order energy responses. The imaginary part of the 1st-order ac specific heat has a broad peak corresponding to the distribution of the eigenvalues.When the temperature is decreased below T g , the frequency of the peak decreases and the width increases. Furthermore, the statistics of eigenvalues can be obtained from the frequency dependence of the 1st-order ac specific heat. The 2nd-order ac specific heat shows extrema as a function of the frequency. The extrema diverge at the Vogel-Fulcher temperature T 0 . The temperature dependence of the extrema changes significantly near T g and some extrema vanish near T x .

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