  In a series of recent papers anomalous Hall and Nernst effects have been
theoretically discussed in the non-linear regime and have seen some early
success in experiments. In this paper, by utilizing the role of Berry curvature
dipole, we derive the fundamental mathematical relations between the anomalous
electric and thermoelectric transport coefficients in the non-linear regime.
The formulae we derive replace the celebrated Wiedemann-Franz law and Mott
relation of anomalous thermoelectric transport coefficients defined in the
linear response regime. In addition to fundamental and testable new formulae,
an important byproduct of this work is the prediction of nonlinear anomalous
thermal Hall effect which can be observed in experiments.
