Entropy current in two dimensional anomalous hydrodynamics and a bound on the sum of the response parameters

Banerjee, Rabin; Dey, Shirsendu; Majhi, Bibhas Ranjan

doi:10.1103/physrevd.92.044019

Cited by 8 publications

(8 citation statements)

References 52 publications

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“…In the absence of a concrete proposal for selecting other terms, we will not pursue the argument any further. Related discussions can be found in [30][31][32][33]. 11…”

Section: The Entropy Currentmentioning

confidence: 99%

Two-dimensional fluids and their holographic duals

et al. 2019

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We describe the dynamics of two-dimensional relativistic and Carrollian fluids. These are mapped holographically to three-dimensional locally anti-de Sitter and locally Minkowski spacetimes, respectively. To this end, we use Eddington-Finkelstein coordinates, and grant general curved two-dimensional geometries as hosts for hydrodynamics. This requires to handle the conformal anomaly, and the expressions obtained for the reconstructed bulk metrics incorporate non-conformal-fluid data. We also analyze the freedom of choosing arbitrarily the hydrodynamic frame for the description of relativistic fluids, and propose an invariant entropy current compatible with classical and extended irreversible thermodynamics. This local freedom breaks down in the dual gravitational picture, and fluid/gravity correspondence turns out to be sensitive to dissipation processes: the fluid heat current is a necessary ingredient for reconstructing all Bañados asymptotically anti-de Sitter solutions. The same feature emerges for Carrollian fluids, which enjoy a residual frame invariance, and their Barnich-Troessaert locally Minkowski duals. These statements are proven by computing the algebra of surface conserved charges in the fluid-reconstructed bulk threedimensional spacetimes.

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“…In the absence of a concrete proposal for selecting other terms, we will not pursue the argument any further. Related discussions can be found in [30][31][32][33]. 11…”

Section: The Entropy Currentmentioning

confidence: 99%

Two-dimensional fluids and their holographic duals

et al. 2019

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“…Since the boundary is two-dimensional, the orthogonal space to the fluid velocity is the one-dimensional space spanned by the Hodge dual of the velocity itself. The decomposition of tensors along these two directions, as already applied in [57,102], is a convenient property in two dimensions.…”

Section: Derivative Expansionmentioning

confidence: 99%

Fefferman--Graham and Bondi Gauges in the Fluid/Gravity Correspondence

Ciambelli¹,

Marteau²,

Petropoulos³

et al. 2020

Proceedings of Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2019)

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In three-dimensional gravity, we discuss the relation between the Fefferman-Graham gauge, the Bondi gauge and the Eddington-Finkelstein type of gauge, often referred to as the derivative expansion, involved in the fluid/gravity correspondence. Starting with a negative cosmological constant, for each gauge, we derive the solution space and the residual gauge diffeomorphisms. We construct explicitly the diffeomorphisms that relate the various gauges, and establish the precise matching of their boundary data. We show that Bondi and Fefferman-Graham gauges are equivalent, while the fluid/gravity derivative expansion, originating from a partial gauge fixing, exhibits an extra unspecified function that encodes the boundary fluid velocity. The Bondi gauge turns out to describe a subspace of the derivative expansion's solution space, featuring a fluid in a specific hydrodynamic frame. We pursue our analysis with the Ricci-flat limit of the Bondi gauge and of the fluid/gravity derivative expansion. The relations between them persist in this limit, which is well-defined and non-trivial. Moreover, the flat limit of the derivative expansion maps to the ultra-relativistic limit on the boundary. This procedure allows to unravel the holographic properties of the Bondi gauge for vanishing cosmological constant, in terms of its boundary Carrollian dual fluid.

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“…Therein, entropy current plays a very important role because, as its divergence ought to be positive, its form entails the constitutive equations of the conserved currents (stress-energy tensor, charged currents) as a function of the gradients of the intensive thermodynamic parameters. Over the last decade, there has been a very large number of studies where the structure of the entropy current in relativistic hydrodynamics was involved, whose a small sample is reported in the bibliography [2][3][4][5][6][7][8][9]. On the other hand, there have been attempts [10] to formulate relativistic hydrodynamics without an entropy current.…”

Section: Introductionmentioning

confidence: 99%

Extensivity, entropy current, area law, and Unruh effect

Becattini

Rindori

2019

Phys. Rev. D

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We present a general method to determine the entropy current of relativistic matter at local thermodynamic equilibrium in quantum statistical mechanics. Provided that the local equilibrium operator is bounded from below and its lowest lying eigenvector is non-degenerate, it is proved that, in general, the logarithm of the partition function is extensive, meaning that it can be expressed as the integral over a 3D space-like hypersurface of a vector current, and that an entropy current exists. We work out a specific calculation for a non-trivial case of global thermodynamic equilibrium, namely a system with constant comoving acceleration, whose limiting temperature is the Unruh temperature. We show that the integral of the entropy current in the right Rindler wedge is the entanglement entropy.

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Entropy current in two dimensional anomalous hydrodynamics and a bound on the sum of the response parameters

Cited by 8 publications

References 52 publications

Two-dimensional fluids and their holographic duals

Two-dimensional fluids and their holographic duals

Fefferman--Graham and Bondi Gauges in the Fluid/Gravity Correspondence

Extensivity, entropy current, area law, and Unruh effect

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