  Symmetry relations are manifestations of fundamental principles and
constitute cornerstones of modern physics. An example are the Onsager relations
between coefficients connecting thermodynamic fluxes and forces, central to
transport theory and experiments. Initially formulated for classical systems,
these reciprocity relations are also fulfilled in quantum conductors.
Surprisingly, novel relations have been predicted specifically for
thermoelectric transport. However, whereas these thermoelectric reciprocity
relations have to date not been verified, they have been predicted to be
sensitive to inelastic scattering, always present at finite temperature. The
question whether the relations exist in practice is important for
thermoelectricity: whereas their existence may simplify the theory of complex
thermoelectric materials, their absence has been shown to enable, in principle,
higher thermoelectric energy conversion efficiency for a given material
quality. Here we experimentally verify the thermoelectric reciprocity relations
in a four-terminal mesoscopic device where each terminal can be electrically
and thermally biased, individually. The linear response thermoelectric
coefficients are found to be symmetric under simultaneous reversal of magnetic
field and exchange of injection and emission contacts. Intriguingly, we also
observe the breakdown of the reciprocity relations as a function of increasing
thermal bias. Our measurements thus clearly establish the existence of the
thermoelectric reciprocity relations, as well as the possibility to control
their breakdown with the potential to enhance thermoelectric performance
