  The consequences of microreversibility for the linear and nonlinear transport
properties of systems subjected to external magnetic fields are systematically
investigated in Aharonov-Bohm rings connected to two, three, and four
terminals. Within the independent electron approximation, the cumulant
generating function, which fully specifies the statistics of the nonequilibrium
currents, is expressed in terms of the scattering matrix of these circuits. The
time-reversal symmetry relations up to the third responses of the currents and
the fourth cumulants are analytically investigated and numerically tested as a
function of the magnetic flux. The validity of such relations is thus firmly
confirmed in this class of open quantum systems.
