Journal
PHYSICAL REVIEW D
Volume 105, Issue 10, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.105.106014
Keywords
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Funding
- Swiss National Science Foundation [200020-182513, 51NF40-141869]
- Republic of Geneva
- Canton of Geneva
- Swiss National Science Foundation (SNF) [51NF40_141869, 200020_182513] Funding Source: Swiss National Science Foundation (SNF)
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The thermodynamic Euler equation for high-energy states of large-N gauge theories is derived in this study. It is shown that this equation is dual to the generalized Smarr formula for black holes in the presence of a negative cosmological constant. Additionally, the fundamental variational equation of thermodynamics is matched to the first law of black hole mechanics, including variations of the cosmological constant and Newton's constant.
The thermodynamic Euler equation for high-energy states of large-N gauge theories is derived from the dependence of the extensive quantities on the number of colors N. 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.
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