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Entropy, holography and the second law

PERIMETER INSTITUTE FOR THEORETICAL PHYSICS. Entropy, holography and the second law. Daniel R. Terno. Subjects:. entropy temperature. Purpose:. to increase our confusion about. holographic principle generalized second law. Non-covariance of entropy. Warning:.

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Entropy, holography and the second law

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  1. PERIMETER INSTITUTE FOR THEORETICAL PHYSICS Entropy, holography and the second law Daniel R. Terno

  2. Subjects: entropy temperature Purpose: to increase our confusion about holographic principle generalized second law Non-covariance of entropy Warning: Number of degrees of freedom Entropy & temperature

  3. Entropy Shannon von Neumann Meaning: minimum over all possible measurements (=POVM) more entropies…

  4. Relative entropy classical measure of distinguishability quantum Perfectly distinguishable states:  Microcanonical entropy data compression quantum data compression # of degrees of freedom Temperature # degrees of freedom

  5. here there there Geometric/entanglement entropy trace out “there” Bombelli et al, Phys. Rev. D34, 373 (1986) Holzhey, Larsen and Wilczek, Nucl. Phys. B424, 443 (1994) Callan and Wilczek, Phys. Lett. B333, 55 (1994). here there

  6. Entropy: non-covariance = ? no correlations no Bell-type violations not irreducible Transformations do not split into here and there spaces

  7. Simple example No transformation law for reduced density matrices Noncovariance of spin entropy Peres and Terno, Rev. Mod. Phys. 76, 93 (2004)

  8. Degrees of freedom: ambiguity Bekenstein, Lett. Nuovo Cim. 4, 737 (1972) …. Busso, Rev. Mod. Phys. 74,825 (2002) Yurtsever, Phys. Rev. Lett. 91, 041302 (2003) Lorentz boost: factors 1/γ # of degrees of freedom is frame-dependent

  9. Entropy: renormalization bosons: Unruh effect General: cut-off Holzhey, Larsen and Wilczek, Nucl. Phys. B424, 443 (1994) D. Marolf, D. Minic, and S. F. Ross, hep-th/0310022. Relative entropy ?

  10. Cosmic thermo Bekenstein Temperature & & Unruh effect & a bit more Jacobson, Phys. Rev. Lett. 75, 1260 (1995)

  11. t Unruh + (k,-m) Audretsch and Müller, Phys. Rev. D 49, 4056 (1994) (k’,m’) (-k’,m’) wavepacket basis x (k,m) Matter outside the horizon n particles in the mode (k,m)

  12. Special case renormalized quantities temperature Of what? General: isTemperature undefined ? two subsystems

  13. Questions Transplantability What to do without T? Corrections to Einstein equations?

  14. Thanks to Charlie Bennett Florian Girelli Netanel Lindner Rob Myers David Poulin Terry Rudolph Lee Smolin Rafael Sorkin

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