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Entropy, holography and the second law

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Entropy, holography and the second law. Daniel R. Terno. PERIMETER ... Perfectly distinguishable states: Microcanonical entropy. Temperature. data compression ... – PowerPoint PPT presentation

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Title: Entropy, holography and the second law


1
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
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/?
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 is Temperature 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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