  Nonlinear anomalous Hall effect is the Berry curvature dipole induced
second-order Hall voltage or temperature difference in response to a
longitudinal electric field or temperature gradient. These are the prominent
Hall responses in time reversal symmetric systems. Here, we investigate the
family of second-order nonlinear anomalous Hall effects, the electrical,
thermoelectric and thermal nonlinear Hall effects in the moir\'e system of
twisted double bilayer graphene. We demonstrate that the nonlinear anomalous
Hall signals can be used to probe the topological phase-transitions in moir\'e
systems, induced by a perpendicular electric field. Specifically, we show that
the whole family of nonlinear anomalous Hall responses undergo a sign reversal
across a topological phase-transition.
