Chemical Potential in the First Law for Holographic Entanglement Entropy

Abstract

Entanglement entropy in conformal field theories is known to satisfy a first law. For spherical entangling surfaces, this has been shown to follow via the AdS/CFT correspondence and the holographic prescription for entanglement entropy from the bulk first law for Killing horizons. The bulk first law can be extended to include variations in the cosmological constant $\Lambda$, which we established in earlier work. Here we show that this implies an extension of the boundary first law to include varying the number of degrees of freedom of the boundary CFT. The thermodynamic potential conjugate to $\Lambda$ in the bulk is called the thermodynamic volume and has a simple geometric formula. In the boundary first law it plays the role of a chemical potential. For the bulk minimal surface $\Sigma$ corresponding to a boundary sphere, the thermodynamic volume is found to be proportional to the area of $\Sigma$, in agreement with the variation of the known result for entanglement entropy of spheres. The dependence of the CFT chemical potential on the entanglement entropy and number of degrees of freedom is similar to how the thermodynamic chemical potential of an ideal gas depends on entropy and particle number.

arXiv comment18 pages; v2 - reference added

References in corpus (14)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• The Holographic Weyl anomaly
• P-V criticality of charged AdS black holes
• Enthalpy and the Mechanics of AdS Black Holes
• Gravitation from Entanglement in Holographic CFTs
• Relative Entropy and Holography
• Holographic Heat Engines
• Smarr Formula and an Extended First Law for Lovelock Gravity
• Entanglement Temperature and Entanglement Entropy of Excited States
• On the conformal anomaly from higher derivative gravity in AdS/CFT correspondence
• Bose condensation and branes
• Tension Perturbations of Black Brane Spacetimes
• Komar Integrals in Higher (and Lower) Derivative Gravity

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