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The Lorenz number (L) contained in the Wiedemann-Franz law represents theratio of two kinetic parameters of electronic charge carriers: the electroniccontribution to the thermal conductivity (K_el) and the electrical conductivity(sigma), , and can be expressed as LT=K_el/sigma where T is temperature. Wedemonstrate that the Lorenz number simply equals to the ratio of twothermodynamic quantities: the electronic heat capacity (c_el) and theelectrochemical capacitance (c_N) through LT=c_el/c_N , a purely thermodynamicquantity, and thus it can be calculated solely based on the electron density ofstates of a material. It is shown that our thermodynamic formulation for theLorenz number leads to: i) the well-known Sommerfeld value L=pi^2/3(k_B/e)^2 atthe low temperature limit, ii) the Drude value L=3/2(k_B/e)^2 at the hightemperature limit with the free electron gas model, and iii) possible highervalues than the Sommerfeld limit for semiconductors. It is also demonstratedthat the purely electronic contribution to the thermoelectric figure-of-meritcan be directly computed using high-throughput DFT calculations withoutresorting to the computationally more expensive Boltzmann transport theory tothe electronic thermal conductivity and electrical conductivity.

Lorenz Number and Electronic Thermoelectric Figure of Merit: Thermodynamics and Direct DFT Calculations