Unifying thermopower: entropy and specific heat in magnetic, superconducting, nanoscale, and frustrated systems.

Thermopower, a key parameter in thermoelectric performance, is often linked to either specific heat or entropy, yet the governing quantity has remained elusive. Here we present a unified framework showing that entropy per carrier, not specific heat, is the universal driver of thermopower in both closed and open systems. Using thermodynamic identities and the Onsager-Kelvin relation, we demonstrate that apparent links to specific heat arise only when heat capacity follows a power-law temperature dependence. Extending the framework, we derive a general expression for magnon-drag thermopower valid for both massive (ferromagnetic) and massless (antiferromagnetic) magnons using a relativistic energy-momentum tensor. We also explore how frustration, flat-band physics, and altermagnetism can sustain entropy at low temperatures or generate Berry-curvature-driven transport, indirectly enhancing thermopower. Case studies of magnetic materials, superconducting niobium, and single-molecule junctions validate the framework, establishing entropy per carrier as a unifying principle for next-generation thermoelectric materials.