From thermodynamics to the bound on viscosity

2009/04/18 by Shahar Hod · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Conformal map #Cosmology and Gravitation Theories #Entropy (arrow of time) #Mathematical analysis #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Physics #Second law of thermodynamics #Statistical physics #Theoretical physics #Thermodynamics #Upper and lower bounds #Viscosity #hep-th

paper · pdf · doi:10.1016/j.nuclphysb.2009.04.008

published as Nucl.Phys.B819:177-182,2009 · 4 pages

openalex publication_date 2009/04/18 · arxiv created 2009/07/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 η/s +O(η³/s³)≥ 1/4π. Furthermore, for conformal field theories we obtain a new fundamental bound on the value of the relaxation coefficient τ_π of causal hydrodynamics, which has been the focus of much recent attention: (τ_πT)²≥ (√(3)-1)/2π².

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• Viscosity bound versus the universal relaxation bound