Thermoelectricity beyond local and instantaneous approximations

Thermoelectricity was a cornerstone in near- equilibrium irreversible thermodynamics. Conversely, classical irreversible thermodynamics (CIT) with its local equilibrium hypothesis (LEH) remains the dominating framework in thermoelectricity. In this talk two instances where CIT approach fails will be presented. Defect engineering is used to control materials thermal conductivity κ, and multiple morphological defects were reported to effectively serve the scope, suppressing phonons with various mean free paths. We studied how grain boundaries and dispersed nanovoids reduce Si κ. The co-presence of defects with different scattering lengths were confirmed to reduce κ. However, application of Matthiessen's rule even to non-gray phonon models led to inconsistencies, showing that non-local descriptors are needed to account for κ modulation. Non-instantaneous response takes a major share in time-dependent thermoelectric phenomena. While the topic is receiving growing attention, still it is mostly framed within CIT, neglecting the disputable validity of the LEH for stimuli with characteristic times comparable to system relaxation times. An approach based on extended irreversible thermodynamics (EIT) will be sustained. However, complete EIT constitutive relations are not yet available for thermoelectricity. This state of affairs will be reviewed and the hurdles hindering the writing of evolutionary equations for thermoelectricity will be commented upon along with recent results.