First-principles theory of ionic thermoelectricity

Symmetry plays a crucial role in shaping the theories of fundamental forces. For example, general covariance -- the equivalence of all possible coordinate systems of spacetime -- dictates the law of gravity. Here, we extend this concept to nonequilibrium thermodynamics by developing a theory of ionic thermoelectricity (thermoelectricity without electrons) in electronically gapped ionic conductors. Within the Green-Kubo formalism, we show that energy gauge invariance -- the equivalence of all possible ways of distributing energy among atoms -- primarily determines the expressions for ionic thermoelectric coefficients. This symmetry-dictated theory is generally applicable, regardless of specific ion transport mechanisms, and provides a rigorous conceptual and computational framework for describing ionic thermoelectricity from first principles.