Experimental Test of the Kelvin Relation Far from Equilibrium

The Kelvin relation (KR), expressed as  π = αT, relates the Peltier Coefficient (π ), thermopower (α) and absolute temperature (T) in thermoelectric (TE) physics. The KR is a specific case of an Onsager Reciprocal Relation (ORR), a cornerstone principle in nonequilibrium thermodynamics. The derivation of the ORR, and therefore KR, explicitly assumes “near-equilibrium” conditions via the local equilibrium assumption (LEA). It remains unknown to what extent the KR may remain applicable for TE systems in “far-from-equilibrium” conditions where use of the LEA becomes questionable. We will present an experimental investigation of the KR beyond the near-equilibrium regime by directly measuring the ratio (π /α) and relating it to T in a set of thermopiles using doped silicon “nano blades” (80 nm wide x 350 nm tall x 700 nm long) as the TE elements. The experimental protocol used temperature gradients large enough that 10-40% deviations could be expected compared to theoretical values dependent on strict validity of the LEA. Our empirical results show relative deviations   |(π /α) – T|/T <2%, within the experimental uncertainty. This suggests the KR and by extension the ORR may continue to be quantitatively correct well beyond the near-equilibrium conditions assumed in their derivation.