Perspective: Nonlinear approaches to structure and dynamics of soft materials

Nonlinear dielectric effects have been the subject of research for over 100 years. A recent surge of activities devoted to this field focuses on soft condensed materials, where interactions and collective dynamics play an important role. The hope is to gain deeper insight into the origin of non-exponential responses and super-Arrhenius behavior, and identify dynamical correlations and connections between dynamics and thermodynamic potentials. While relaxation spectroscopy can reveal details of the dynamics across an impressive range of time scales, many interesting features remain obscured if limited to the regime of linear response. This perspective portrays the recent progress in the field of nonlinear dynamics, with focus on the complex dynamics of supercooled liquids with departures not too far from equilibrium. Nonlinear dielectric effects will be highlighted and compared with the mechanical and calorimetric counterparts.