Recent progress in the free energy landscape theory and its application to aging and slow Arrhenius process

The Helmholtz free energy landscape (FEL) picture is known to provide a theoretical framework which can explain various aspects of non-equilibrium systems. I first show that the landscape for various thermodynamic potentials including enthalpy and Gibbs free energy can be properly defined. In order to find physics behind two complex phenomena observed in non-equilibrium systems, protocol-dependent aging and the slow Arrhenius process (SAP), I introduce phenomenologically a delayed response of the FEL to a perturbation. As for the aging, the delayed response to temperature change is shown to produce protocol-dependent aging which cannot be explained by the standard trap model of aging. In order to explain physics of the SAP observed in dielectric relaxations, I introduce a delayed response of the FEL to a sinusoidal electric field and show that the delayed response can give rise to a slow process similar to the SAP.