  In mesoscopic systems to study the role of inelastic scattering on the phase
coherent motion of electrons two phenomenological models have been proposed. In
the first one, due to B\"uttiker, one adds a voltage probe into the system (or
in the scattering matrix). The second model invokes the complex (or optical)
potential in the system Hamiltonian. Studying a simple geometry of a metallic
loop in the presence of Aharonov-Bohm magnetic flux, we show that the two probe
conductance is symmetric in the reversal of the magnetic field in B\"uttiker's
approach. Whereas the two probe conductance within the complex potential model
is asymmetric in the magnetic flux reversal contrary to the expected behavior.
