  Aspects of the low energy physics of certain Jackiw-Teitelboim gravity and
supergravity theories are explored, using their recently presented
non-perturbative description in terms of minimal string models. This regime
necessarily involves non-perturbative phenomena, and the inclusion of wormhole
geometries connecting multiple copies of the nearly AdS$_2$ boundary in the
computation of ensemble averages of key quantities. A new "replica-scaling"
limit is considered, combining the replica method and double scaling with the
low energy limit. Using it, the leading free energy, entropy, and specific heat
are explored for various examples. Two models of particular note are the JT
supergravity theory defined as a (1,2) Altland-Zirnbauer matrix ensemble by
Stanford and Witten, and the Saad-Shenker-Stanford matrix model of ordinary JT
gravity (non-perturbatively improved at low energy). The full models have a
finite non-vanishing spectral density at zero energy. The replica-scaling
construction suggests for them a low temperature entropy and specific heat that
are linear in temperature.
