A coarse-grained generalized second law for holographic conformal field theories

作者：Bunting William; Fu Zicao; Marolf Donald^*

来源：Classical and Quantum Gravity, 2016, 33(5): 055008.

DOI：10.1088/0264-9381/33/5/055008

• generalized second law
• holographic entropy
• holographic quantum field theory

We consider the universal sector of a d > 2 dimensional large-N strongly interacting holographic CFT on a black hole spacetime background B. When our CFTd is coupled to dynamical Einstein-Hilbert gravity with Newton constant G(d), the combined system can be shown to satisfy a version of the thermodynamic generalized second law (GSL) at leading order in G(d). The quantity S-CFT + A(H-B,H- perturbed)/4G(d) is non-decreasing, where A(H-B,H- perturbed) is the (time-dependent) area of the new event horizon in the coupled theory. Our S-CFT is the notion of (coarse-grained) CFT entropy outside the black hole given by causal holographic information-a quantity in turn defined in the AdS(d+1) dual by the renormalized area A(ren)(H-bulk) of a corresponding bulk causal horizon. A corollary is that the fine-grained GSL must hold for finite processes taken as a whole, though local decreases of the fine-grained generalized entropy are not obviously forbidden. Another corollary, given by setting G(d) = 0, states that no finite process taken as a whole can increase the renormalized free energy F = E-out - TSCFT - Omega J, with T, Omega constants set by H-B. This latter corollary constitutes a 2nd law for appropriate non-compact AdS event horizons.

• 出版日期2016-3-3
• 单位清华大学