In this talk, I will discuss two entropic puzzles in Jackiw–Teitelboim gravity (JT gravity) and their resolution, which requires incorporating non-perturbative effects in the gravitational path integral.
The first puzzle concerns the low-temperature behavior of the thermal entropy. In JT gravity—dual to a random matrix ensemble—the gravitational entropy can become negative at very low temperatures when computed as an annealed quantity rather than a quenched one. This signals a breakdown of expected thermodynamic behavior, in tension with the third law of thermodynamics. I will show how defining an intermediate “semi-quenched” entropy restores consistency. From the bulk perspective, this involves a resummation of higher-genus topologies and wormhole contributions, while from the matrix model perspective the resolution is governed by edge eigenvalue statistics, described by the Airy distribution and by one-eigenvalue instantons. I will also comment on similarities and differences with the Sachdev-Ye-Kitaev (SYK) model, which provides a more structured boundary theory.
A related puzzle arises in the entanglement entropy of two-sided black holes, which can become negative when a large number of matter excitations are inserted behind the horizon. First identified by Lin-Maldacena-Rosenberg-Shan in supersymmetric JT gravity, I will show that this paradox persists in non-supersymmetric JT gravity with matter, and demonstrate how positivity is restored in both settings. Finally, I will present a random tensor network toy model that exhibits the same phenomena, providing a complementary perspective on these effects.