The cosmological constant is treated as a thermodynamical parameter in the framework of two-dimensional dilaton gravity. We find that the cosmological constant behaves as a $U(1)$ charge with a confining potential, and that such potentials require a novel Born-Infeld boundary term in the action. The free energy and other thermodynamical quantities of interest are derived, from first principles, in a way that is essentially model independent. We discover that there is always a Schottky anomaly in the specific heat and explain its physical origin. Finally, we apply these results to specific examples, like anti-de Sitter–Schwarzschild–Tangherlini black holes, Bañados-Teitelboim-Zanelli black holes and the Jackiw-Teitelboim model.

• Received 4 July 2014

DOI:https://doi.org/10.1103/PhysRevD.90.044032