Thermodynamic duality between RN black hole and 2D dilaton gravity

All thermodynamic quantities of the Reissner-Nordstr"om (RN) black hole can be obtained from the dilaton and its potential of two dimensional (2D) dilaton gravity. The dual relations of four thermodynamic laws are also established. Furthermore, the near-horizon thermodynamics of the extremal RN black hole is completely described by the Jackiw-Teitelboim theory which is obtained by perturbing around the AdS${}_2$-horizon.