Holographic Thermodynamics Requires a Chemical Potential for Color

Abstract

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.

9 pages, v4: matches published version in PRD, added clarification on thermal free energy charge

References in corpus (12)

• Towards a derivation of holographic entanglement entropy
• Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume
• Holographic c-theorems in arbitrary dimensions
• Seeing a c-theorem with holography
• Universal Spectrum of 2d Conformal Field Theory in the Large c Limit
• Smarr Formula and an Extended First Law for Lovelock Gravity
• Phase transition and Thermodynamical geometry of Reissner-Nordström-AdS Black Holes in Extended Phase Space
• Phase transition and thermodynamical geometry for Schwarzschild AdS black hole in $Ad{S}_5\times S^5$ spacetime
• Bose condensation and branes
• Chemical Potential in the First Law for Holographic Entanglement Entropy
• Higher Order Corrections to Holographic Black Hole Chemistry
• The first law of differential entropy and holographic complexity

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