  We calculate amplitudes for 2D vacuum transitions by means of the Euclidean
methods of Coleman-De Luccia (CDL) and Brown-Teitelboim (BT), as well as the
Hamiltonian formalism of Fischler, Morgan and Polchinski (FMP). The resulting
similarities and differences in between the three approaches are compared with
their respective 4D realisations. For CDL, the total bounce can be expressed as
the product of relative entropies, whereas, for the case of BT and FMP, the
transition rate can be written as the difference of two generalised entropies,
ultimately enabling to circumvent the need to resort to detailed balance. By
means of holographic arguments, we show that the Euclidean methods, as well as
the Lorentzian cases without non-extremal black holes, provide examples of an
AdS$_2$/CFT$_1 \subset $ AdS$_3$/CFT$_2$ correspondence. Such embedding is not
possible in the presence of islands for which the setup corresponds to
AdS$_2$/CFT$_1 \not\subset $ AdS$_3$/CFT$_2$. We find that whenever an island
is present, up-tunnelling is possible.
