Relaxation of the free energy landscape and temperature modulation spectroscopy

Abstract The free energy landscape (FEL) depends on temperature by its definition and the FEL is reorganized with time delay when the temperature is modulated. We investigate how the relaxation of the FEL manifests itself in physical properties. Exploiting a simple two-level model for the dielectric relaxation, we first show that the relaxation of the FEL produces time dependence of the relaxation time of the dielectric response. Then we discuss the relaxation of dielectric susceptibility when the temperature is suddenly increased/decreased and show that the susceptibility relaxes to the equilibrium value with the same relaxation time as the FEL in the long time limit. In order to show the general feature of the temperature modulation spectroscopy, we consider the dynamics of an order parameter of the Landau model which has a delayed response to the temperature modulation with relaxation time. When the temperature is modulated sinusoidally, we show that there appear second order responses at the sum and the difference of the frequencies of the external field and the temperature modulation and that the relaxation time of the FEL can be deduced from these two responses.