Universal viscosity to entropy density ratio from entanglement

Journal Article · Thu Jul 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.82.024010· OSTI ID:21410120

Chirco, Goffredo; Eling, Christopher; Liberati, Stefano ^[1]

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1. SISSA, Via Bonomea 265, 34136 Trieste (Italy) and INFN Sezione di Trieste, Via Valerio 2, 34127 Trieste (Italy)

We present evidence that the universal Kovtun-Son-Starinets shear viscosity to entropy density ratio of 1/4{pi} can be associated with a Rindler causal horizon in flat spacetime. Since there is no known holographic (gauge/gravity) duality for this spacetime, a natural microscopic explanation for this viscosity is in the peculiar properties of quantum entanglement. In particular, it is well known that the Minkowski vacuum state is a thermal state and carries an area entanglement entropy density in the Rindler spacetime. Based on the fluctuation-dissipation theorem, we expect a similar notion of viscosity arising from vacuum fluctuations. Therefore, we propose a holographic Kubo formula in terms of a two-point function of the stress tensor of matter fields in the bulk. We calculate this viscosity assuming a minimally coupled scalar field theory and find that the ratio with respect to the entanglement entropy density is exactly 1/4{pi} in four dimensions. The issues that arise in extending this result to nonminimally coupled scalar fields, higher spins, and higher dimensions provide interesting hints about the relationship between entanglement entropy and black hole entropy.

• OSTI ID: 21410120
• Journal Information: Physical Review. D, Particles Fields, Vol. 82, Issue 2; Other Information: DOI: 10.1103/PhysRevD.82.024010; (c) 2010 The American Physical Society; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BLACK HOLES
DENSITY
DUALITY
ENTROPY
FLUCTUATIONS
GRAVITATION
HOLOGRAPHY
KUBO FORMULA
MINKOWSKI SPACE
QUANTUM ENTANGLEMENT
SCALAR FIELDS
SPACE-TIME
SPIN
VACUUM STATES
VISCOSITY
ANGULAR MOMENTUM
MATHEMATICAL SPACE
PARTICLE PROPERTIES
PHYSICAL PROPERTIES
SPACE
THERMODYNAMIC PROPERTIES
VARIATIONS