Thermoelectric phenomena via an interacting particle system

TL;DR

This paper introduces a mesoscopic lattice model for thermoelectric effects, capturing heat and charge transport phenomena like Seebeck and Peltier effects, and derives their linear response relations using an interacting particle system framework.

Contribution

It extends the simple exclusion process to model thermoelectric phenomena, deriving linear response relations and higher order corrections within a unified particle system approach.

Findings

Derivation of Seebeck and Peltier coefficients relations

Model reproduces equilibrium Fermi-Dirac distribution

Characterization of entropy production in the system

Abstract

We present a mesoscopic model for thermoelectric phenomena in terms of an interacting particle system, a lattice electron gas dynamics that is a suitable extension of the standard simple exclusion process. We concentrate on electronic heat and charge transport in different but connected metallic substances. The electrons hop between energy-cells located alongside the spatial extension of the metal wire. When changing energy level, the system exchanges energy with the environment. At equilibrium the distribution satisfies the Fermi-Dirac occupation-law. Installing different temperatures at two connections induces an electromotive force (Seebeck effect) and upon forcing an electric current, an additional heat flow is produced at the junctions (Peltier heat). We derive the linear response behavior relating the Seebeck and Peltier coefficients as an application of Onsager reciprocity. We also indicate the higher order corrections. The entropy production is characterized as the anti-symmetric part under time-reversal of the space-time Lagrangian.