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Black Holes and the Fluctuation Theorem

Black Holes and the Fluctuation Theorem . Susumu Okazawa ( 総研大 , KEK) with Satoshi Iso and Sen Zhang , arXiv:1008.1184 + work in progress. Backgrounds Gravity Black hole thermodynamics Hawking radiation – classical gravity + quantum field

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Black Holes and the Fluctuation Theorem

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  1. Black Holes and the Fluctuation Theorem Susumu Okazawa(総研大,KEK) withSatoshi Isoand Sen Zhang, arXiv:1008.1184 +work in progress

  2. Backgrounds Gravity • Black hole thermodynamics • Hawking radiation • – classical gravity + quantum field – Planck distribution with temperature • What about non-equilibrium? • – Asymptotically flat Schwarzschild BHs are unstable system, “negative specific heat” Susumu Okazawa (KEK)

  3. Backgrounds Non-equilibrium physics • The Fluctuation Theorem [Evans, Cohen & Morris ‘93] • – non-equilibrium fluctuations satisfy • – violation of the second law of thermodynamics • The fluctuation theorem The second law of thermodynamics • Microscopic, Equality Macroscopic, Inequality • – A bridge between microscopic theory with time reversal symmetry • andthe second law of thermodynamics Susumu Okazawa (KEK)

  4. Motivations • We want to investigate non-equilibrium nature of black holes • – cf. Einstein’s theory of Brownian motion, fluctuations are important • – Analyzing an asymptotically flat BH as a thermodynamically unstable system • We apply the fluctuation theorem to BH with matter • – We expect to see entropy decreasing probability • – We expect to get the generalized second law as a corollary • Ambitions • – Information loss problem • – Connection between Jacobson’s idea “the Einstein equation of states” • – Application for gauge/gravity duality Susumu Okazawa (KEK)

  5. Outline • We will consider a spherically symmetric BH with scalar field • Construct an effective EOM of scalar field near the horizon • cf. real -time AdS/CFT [Herzog, Son ’03 , Son, Teaney ‘09] Ingoing boundary condition (friction) Hawking radiation (noise) Langevin equation Susumu Okazawa (KEK)

  6. Outline • By using 1st law • Microscopic • Equality The fluctuation theorem for BH and matter • Macroscopic • Inequality The generalized second law • Green-Kubo relation Extension to non-linear response Response correlation Susumu Okazawa (KEK)

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