  Topological Josephson junctions carry 4pi-periodic bound states. A finite
bias applied to the junction limits the lifetime of the bound state by
dynamically coupling it to the continuum. Another characteristic time scale,
the phase adjustment time, is determined by the resistance of the circuit
"seen" by the junction. We show that the 4pi periodicity manifests itself by an
even-odd effect in Shapiro steps only if the phase adjustment time is shorter
than the lifetime of the bound state. The presence of a peak in the current
noise spectrum at half the Josephson frequency is a more robust manifestation
of the 4pi periodicity, as it persists for an arbitrarily long phase adjustment
time. We specify, in terms of the circuit parameters, the conditions necessary
for observing the manifestations of 4pi periodicity in the noise spectrum and
Shapiro step measurements.
