When Spectroscopies Speak the Same Language: Unifying Rheology, Electrochemical Impedance, and Dielectrics.

Spectroscopic techniques measure the dynamical response of physical systems subjected to oscillatory perturbations. For small perturbations around the equilibrium state, these spectroscopic methods are unified by the common mathematical framework of linear response theory. This work presents a unified perspective on rheological or mechanical spectroscopy, electrochemical impedance spectroscopy, and broadband dielectric spectroscopy through the lens of linear response theory. Subtle conceptual similarities and differences among these techniques are highlighted by analyzing their mapping to the linear response theory, basic building blocks, elementary models, and time and frequency domain response functions. Data validation and analysis approaches, including Kramers-Kronig relations, equivalent circuits, and multimode models are discussed. The shared fundamentals of different spectroscopies enable seamless exchange of ideas across domains.