  We have identified anomalous behavior of the escape rate out of the
zero-voltage state in Josephson junctions with a high critical current density
Jc. For this study we have employed YBa2Cu3O7-x grain boundary junctions, which
span a wide range of Jc and have appropriate electrodynamical parameters. Such
high Jc junctions, when hysteretic, do not switch from the superconducting to
the normal state following the expected stochastic Josephson distribution,
despite having standard Josephson properties such as a Fraunhofer magnetic
field pattern. The switching current distributions (SCDs) are consistent with
nonequilibrium dynamics taking place on a local rather than a global scale.
This means that macroscopic quantum phenomena seem to be practically
unattainable for high Jc junctions. We argue that SCDs are an accurate means to
measure nonequilibrium effects. This transition from global to local dynamics
is of relevance for all kinds of weak links, including the emergent family of
nanohybrid Josephson junctions. Therefore caution should be applied in the use
of such junctions in, for instance, the search for Majorana fermions.
