What Really Drives Thermopower: Specific Heat or Entropy as the Unifying Principle Across Magnetic, Superconducting, and Nanoscale Systems

TL;DR

This paper establishes entropy per carrier as the fundamental principle governing thermopower across various systems, unifying magnetic, superconducting, and nanoscale phenomena through a comprehensive thermodynamic framework.

Contribution

It introduces a universal theoretical framework linking thermopower to entropy per carrier, extending it to magnetic systems with a relativistic magnon model, and validates with experimental data.

Findings

Thermopower universally proportional to entropy per carrier.

Magnetic, superconducting, and nanoscale systems follow entropy-based thermopower scaling.

Relativistic magnon model resolves previous conceptual inconsistencies.

Abstract

Thermopower, a key parameter in thermoelectric performance, is often linked to either specific heat or entropy, yet the fundamental quantity that governs it has remained elusive. In this work, we present a unified theoretical framework that identifies entropy per carrier, not specific heat, as the universal driver of thermopower across both closed and open systems. Using thermodynamic identities and the Onsager-Kelvin relation, we show that thermopower is universally proportional to entropy per carrier, while its apparent proportionality to specific heat arises only in systems where the specific heat follows a continuous power-law temperature dependence. To extend this framework to magnetic systems, we derive a general expression for magnon-drag thermopower that holds in both Newtonian (massive, parabolic) and relativistic (massless, linear) magnon regimes. In particular, we reformulate the momentum balance using a relativistic energy-momentum tensor, resolving conceptual inconsistencies in prior models that relied on ill-defined magnon masses in antiferromagnets. Our framework is further illustrated through three representative systems: (i) magnetic materials, where magnon and paramagnon entropy sustain thermopower across TC and TN; (ii) superconducting Nb, where anomalous thermopower emerges from entropy carried by Bogoliubov quasiparticles near TC; and (iii) a single-molecule junction, where entropy from occupation-number fluctuations governs thermopower in an open quantum system. We validate our unifying principle by comparing it with experimental data: thermopower measurements of superconducting niobium reveal the role of quasiparticle entropy near the critical temperature, and literature-reported specific heat data from a wide range of ferromagnetic and antiferromagnetic materials demonstrate consistent entropy-based scaling across magnetic transitions.