  The probe technique is a simple mean to incorporate elastic and inelastic
processes into quantum dynamics. Using numerical simulations, we demonstrate
that this tool can be employed beyond the analytically tractable linear
response regime, providing a stable solution for the probe parameters:
temperature and chemical potential. Adopting four probes: dephasing, voltage,
temperature, and voltage-temperature, mimicking different elastic and inelastic
effects, we focus on magnetic field and gate voltage symmetries of charge
current and heat current in Aharonov-Bohm interferometers, potentially
far-from-equilibrium. Considering electron current, we prove analytically that
in the linear response regime inelastic scattering processes do not break the
Onsager symmetry. Beyond linear response, even (odd) conductance terms obey an
odd (even) symmetry with the threading magnetic flux, as long as the system
acquires a spatial inversion symmetry. When spatial asymmetry is introduced
particle-hole symmetry assures that nonlinear conductance terms maintain
certain symmetries with respect to magnetic field and gate voltage. These
analytic results are supported by numerical simulations. Analogous results are
obtained for the electron heat current. We also demonstrate that a double-dot
Aharonov-Bohm interferometer acts as a rectifier when two conditions are met:
(i) many-body effects are included, here in the form of inelastic scattering,
and (ii) time reversal symmetry is broken.
