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Holographic Thermodynamics Requires a Chemical Potential for Color

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arxiv 2101.04145 v4 pith:VB3EYPAG submitted 2021-01-11 hep-th cond-mat.stat-mechgr-qc

Manus R. Visser This is my paper · ORCID
classification hep-thcond-mat.stat-mechgr-qc
keywords equationconstanteulerblackchemicalcosmologicalgaugenumber
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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.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Holographic heat engines for Schwarzschild black holes

    hep-th 2026-07 accept novelty 6.0 of 10

    Schwarzschild black holes in finite cavities yield fixed-theory reversible heat engines with exact cycle efficiencies that probe quasi-local equations of state.

  2. Topological perspective on bulk boundary thermodynamic equivalence

    hep-th 2025-12 conditional novelty 6.0 of 10

    A two-central-charge CFT dictionary reproduces the extended first law, critical point, and topological charges of the 5D charged Gauss-Bonnet AdS black hole.

  3. Finite-cutoff Holographic Thermodynamics

    hep-th 2025-07 conditional novelty 6.0 of 10

    Finite-cutoff holography yields a thermodynamic duality between T^2-deformed CFTs and Schwarzschild-AdS black holes with a Dirichlet wall, including a teardrop coexistence curve with up to three states at one temperature.

  4. Extended thermodynamical topology of black hole

    hep-th 2025-08 unverdicted novelty 5.0 of 10

    The paper introduces a unified extended thermodynamical topology framework for black holes and claims a correspondence between zeros of higher-order vector fields and critical exponents.

  5. Noncommutative black holes: Topological bulk-boundary correspondence and Binary Merger Bounds

    gr-qc 2026-07 reject novelty 4.0 of 10

    For noncommutative RN-AdS black holes, the paper claims bulk and boundary thermodynamic topological charges equal to zero and derives perturbative second-law corrections to the remnant-mass bound.

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