  In addition to the usual superconducting current, Josephson junctions (JJs)
support a phase-dependent conductance related to the retardation effect of
tunneling quasi-particles. This introduces a dissipative current with a
memory-resistive (memristive) character and thus should also affect the current
noise. By means of the microscopic theory of tunnel junctions we compute the
complete current autocorrelation function of a Josephson tunnel junction and
show that this memristive component gives rise to a non-stationary,
phase-dependent noise. As a consequence, dynamic and thermal noise necessarily
show a phase dependence otherwise absent in nondissipative JJ models. This
phase dependence may be realized experimentally as a hysteresis effect if the
unavoidable time averaging of the experimental probe is shorter than the period
of the Josephson phase.
