Abstract
The thermodynamic Euler equation for high-energy states of large- gauge theories is derived from the dependence of the extensive quantities on the number of colors . This Euler equation relates the energy of the state to the temperature, entropy, number of degrees of freedom and its chemical potential, but not to the volume or pressure. In the context of the gauge/gravity duality we show that the Euler equation is dual to the generalized Smarr formula for black holes in the presence of a negative cosmological constant. We also match the fundamental variational equation of thermodynamics to the first law of black hole mechanics, when extended to include variations of the cosmological constant and Newton’s constant.
- Received 24 January 2021
- Accepted 12 January 2022
DOI:https://doi.org/10.1103/PhysRevD.105.106014
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Published by the American Physical Society