Holographic entropy production

Journal of High Energy Physics, Oct 2014

Abstract The suspicion that gravity is holographic has been supported mainly by a variety of specific examples from string theory. In this paper, we propose that such a holography can actually be observed in the context of Einstein’s gravity and at least a class of generalized gravitational theories, based on a definite holographic principle where neither is the bulk space-time required to be asymptotically AdS nor the boundary to be located at conformal infinity, echoing Wilson’s formulation of quantum field theory. After showing the general equilibrium thermodynamics from the corresponding holographic dictionary, in particular, we provide a rather general proof of the equality between the entropy production on the boundary and the increase of black hole entropy in the bulk, which can be regarded as strong support to this holographic principle. The entropy production in the familiar holographic superconductors/superfluids is investigated as an important example, where the role played by the holographic renormalization is explained.

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Holographic entropy production

Yu Tian 0 1 3 4 6 7 8 9 Xiao-Ning Wu 0 1 3 4 5 7 8 9 Hongbao Zhang 0 1 2 3 7 8 9 0 Beijing 100190, China 1 Institute of Theoretical Physics, Chinese Academy of Sciences 2 Theoretische Natuurkunde, Vrije Universiteit Brussel and The International Solvay Institutes 3 Beijing 100049, China 4 State Key Laboratory of Theoretical Physics 5 Institute of Mathematics, Academy of Mathematics and System Science , CAS 6 School of Physicas, University of Chinese Academy of Sciences 7 Open Access, c The Authors 8 of Quantum Gravity, Quantum Dissipative Systems 9 Pleinlaan 2, B-1050 Brussels, Belgium The suspicion that gravity is holographic has been supported mainly by a variety of specific examples from string theory. In this paper, we propose that such a holography can actually be observed in the context of Einstein's gravity and at least a class of generalized gravitational theories, based on a definite holographic principle where neither is the bulk space-time required to be asymptotically AdS nor the boundary to be located at conformal infinity, echoing Wilson's formulation of quantum field theory. After showing the general equilibrium thermodynamics from the corresponding holographic dictionary, in particular, we provide a rather general proof of the equality between the entropy production on the boundary and the increase of black hole entropy in the bulk, which can be regarded as strong support to this holographic principle. The entropy production in the familiar holographic superconductors/superfluids is investigated as an important example, where the role played by the holographic renormalization is explained. ArXiv ePrint: 1407.8273 1 Introduction 2 Holographic dictionary and its implementation in the equilibrium thermodynamics 2.1 Thermodynamics dual to the RN bulk space-time 2.2 The general thermodynamics by Hamilton-Jacobi-like analysis 3 Entropy production on the holographic screen and its equality with the 3.1 3.2 4.1 increase of entropy in the bulk The case without cross-transportation For more general gravitational theories 3.3 The case with cross-transportation 4 Entropy production in holographic superconductors/superfluids Universal form of the holographic entropy production The second order conserved current From finite cutoff to the conformal boundary 5 Conclusion and discussion A Black-hole thermodynamics with the topological charge B The increase of horizon area from the Raychaudhuri equation 1 Introduction Evidence has accumulated since the end of last century that quantum gravity is holographic [1, 2], i.e. quantum gravity in a (d + 1)-dimensional space-time region can be described by some sort of quantum field theory on the d-dimensional boundary of this region, especially since the discovery of AdS/CFT correspondence [35] in the framework of (super)string theory. On one hand, nowadays there have been many generalizations and/or applications of AdS/CFT correspondence, such as most of the phenomenological models in AdS/CMT (condensed matter theory), AdS/QCD and so on, which cannot be embedded in string theory. On the other hand, besides the black hole thermodynamics [6] that inspires the proposition of holography, there are already various hints from within the context of Einsteins gravity towards the speculation that gravity is essentially holographic, where neither string theory nor supersymmetry are involved. Here we would like list three of them as follows. Brown-Henneauxs asymptotic symmetry analysis for three dimensional gravity [7]. Brown-Yorks surface tensor formulation of quasilocal energy and conserved Boussos covariant entropy bound [9]. In particular, Brown-Yorks surface tensor formulation bears a strong resemblance to the recipe in the dictionary for AdS/CFT correspondence, and has actually been incorporated into the latter (or its generalizations). Holography could have been explicitly implemented just in Einsteins gravity, in fact, if one was brave enough to declare that Brown-Yorks surface tensor is not only for the purpose of the bulk side but also for some sort of system living on the boundary. In AdS/CFT, the radial direction of the (asymptotic AdS) bulk space-time corresponds to the energy scale of the dual field theory [1013] and the change of radial coordinate r is regarded as equivalent to the corresponding renormalization group (RG) flow [1420], from this point of view, the RG flows of many important transport coefficients of the boundary theory (at finite temperature) are trivial, which enables one to compute these coefficients by the so-called black-hole membrane paradigm [21]. Especially, it is proved the RG flow, so the universality of this ratio in both the black-hole membrane paradigm and the standard AdS/CFT follows. In the above framework of the so-called holographic RG flow, physical quantities can be defined on any constant r surface (called the finite cutoff surface), while their RG flows are obtained by changing r. However, the finite cutoff (...truncated)


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Yu Tian, Xiao-Ning Wu, Hongbao Zhang. Holographic entropy production, Journal of High Energy Physics, 2014, pp. 170, Volume 2014, Issue 10, DOI: 10.1007/JHEP10(2014)170