From Thermodynamics to the Bound on Viscosity

Abstract

We show that the generalized second law of thermodynamics may shed much light on the mysterious Kovtun-Son-Starinets (KSS) bound on the ratio of viscosity to entropy density. In particular, we obtain the lower bound $\eta /s+O({\eta }^3/s^3)\ge 1/4\pi$. Furthermore, for conformal field theories we obtain a new fundamental bound on the value of the relaxation coefficient ${\tau }_{\pi }$ of causal hydrodynamics, which has been the focus of much recent attention: $({\tau }_{\pi }T{)}^2\ge (\sqrt{3}-1)/2{\pi }^2$.

4 pages

References in corpus (28)

• Gauge Theory Correlators from Non-Critical String Theory
• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Shear viscosity of strongly coupled N=4 supersymmetric Yang-Mills plasma
• Nonlinear Fluid Dynamics from Gravity
• Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?
• Relativistic viscous hydrodynamics, conformal invariance, and holography
• The Effect of Shear Viscosity on Spectra, Elliptic Flow, and HBT Radii
• Holography and hydrodynamics: diffusion on stretched horizons
• Energy Loss and Flow of Heavy Quarks in Au+Au Collisions at sqrt(s_NN) = 200 GeV
• Viscosity Bound Violation in Higher Derivative Gravity
• Viscosity, Black Holes, and Quantum Field Theory
• Universality of the shear viscosity in supergravity
• Viscosity Bound and Causality Violation
• Simulating elliptic flow with viscous hydrodynamics
• Suppression of elliptic flow in a minimally viscous quark-gluon plasma
• Heating up Galilean holography
• Causal hydrodynamics of gauge theory plasmas from AdS/CFT duality
• Viscous hydrodynamics relaxation time from AdS/CFT
• Universal Bound on Dynamical Relaxation Times and Black-Hole Quasinormal Ringing
• The Shear Viscosity to Entropy Density Ratio of Trapped Fermions in the Unitarity Limit
• Shear viscosity of a superfluid Fermi gas in the unitarity limit
• How does the entropy/information bound work ?
• Holographic Viscosity of Fundamental Matter
• On the supergravity description of boost invariant conformal plasma at strong coupling
• Near-Extreme Black Holes and the Universal Relaxation Bound
• A sticky business: the status of the conjectured viscosity/entropy density bound
• From Unruh temperature to generalized Bousso bound
• The bound on viscosity and the generalized second law of thermodynamics

Cited by in corpus (4)

• A proof of the Bekenstein bound for any strength of gravity through holography
• Information content and minimum-length metric: A drop of light
• Hydrodynamics of strongly coupled non-conformal fluids from gauge/gravity duality
• Viscosity bound versus the universal relaxation bound