  We investigate classical thermal activation (TA) and macroscopic quantum
tunneling (MQT) for a Josephson junction coupled with an LC circuit
theoretically. The TA and MQT escape rate are calculated analytically by taking
into account the two-dimensional nature of the classical and quantum phase
dynamics. We find that the MQT escape rate is largely suppressed by the
coupling to the LC circuit. On the other hand, this coupling gives rise to
slight reduction of the TA escape rate. These results are relevant for the
interpretation of a recent experiment on the MQT and TA phenomena in grain
boundary YBCO Josephson junctions.
