Nonlinear Energy Response to Oscillating Temperature in the Free Energy Landscape Picture

The nonlinear energy response to oscillating temperature is studied for a system described by the free energy landscape picture. It is shown that the 2nd order response has time dependent and time independent terms. The former oscillates with frequency twice as large as the frequency of the temperature perturbation, whose coefficient is called the 2nd order ac specific heat. It is shown that the latter becomes a plateau in the high frequency region. We apply this framework to a model free energy landscape and show that the 2nd order ac specific heat has the extrema which diverge at the Vogel‐Fulcher tempearture T0 and that the temperature dependence of the extrema changes near the glass transition point Tg.