In this talk, I will discuss two entropic puzzles in JT gravity and their resolution, which requires taking into account non-perturbative effects in the gravitational path integral. In JT gravity, which is dual to a random matrix ensemble, the gravitational thermal entropy becomes negative at very low temperatures. This puzzle arises when computing the annealed (instead of quenched) entropy, corresponding to an incorrect averaging procedure in the dual matrix model. After defining an “intermediate” quantity, the semi-quenched entropy, I will explain how the positivity of entropy can be rescued. From the bulk perspective, both a resummation of higher-genus topologies and wormhole effects are crucial. From the matrix model perspective, the resolution relies on the statistics of eigenvalues near the edge, governed, in different regimes, by the Airy distribution or by 1-eigenvalue instantons. A related puzzle arises where the entanglement entropy across a two-sided black hole can become negative when inserting a large number of matter excitations behind the black hole horizon. First posed by Lin, Maldacena, Rosenberg, and Shan in two-sided BPS black holes in SUSY JT gravity, I will show this paradox extends to non-SUSY JT gravity with matter as well and demonstrate how positivity is rescued in both cases. Finally, I will discuss a tensor network toy model with the same features.