Entropy Bounds |
In General
> s.a. boundaries in field theory; holography.
* Idea: An upper limit
for the amount of entropy a system can have; Depending on the context or
motivation, it can be given in terms of the system's energy (Bekenstein)
or size, for example surface area; From considerations based on a fundamental
length, it is normally assumed that quantum gravity implies an upper limit
on the entropy for a bounded region.
* Remark: One possible
objection to the existence of such a bound, the "species problem",
is that as the number of fields considered in a theory grows, so does the
entropy of a region, apparently unboundedly; Addessed by remarking that the
number of fields actually present is (probably) finite, and that if one changes
the number of fields in a theory one can also change the values of the constants
in the bound.
@ General references: Bekenstein PRD(81);
Schiffer & Bekenstein PRD(89);
Zaslavskii CQG(96);
Bousso JHEP(01)ht/00 [in de Sitter and Minkowski];
Bekenstein FP(05)qp/04 [how it works];
Marolf ht/04-GR17 [rev];
Rideout & Zohren CQG(06)gq [from causal sets].
@ Consequences: Karch ht/03 [fluid viscosity bound];
Medved MPLA(06)ht/05 [cosmology, dark energy and inflation].
@ Hyperentropic objects: Marolf & Sorkin PRD(04)ht/03 [Hawking radiation];
Bekenstein PRD(04)ht;
Hod PLB(11)-a1108 [and the generalized second law].
@ Other violations: Page gq/00,
ht/00;
Bekenstein gq/00 [rebuttal];
Page JHEP(08)ht/00 [and fix];
Masoumi & Mathur PRD(15)-a1412 [of the covariant bound].
> Online resources: see Wikipedia pages
on the Bekenstein bound and
Bousso's holographic bound.
Bekenstein Bound
> s.a. Bekenstein-Hod Bound; GUP phenomenology.
* Idea: For a system with
energy E and typical size L, a universal bound on the
entropy is S ≤ 2π EL/c\(\hbar\).
* Result: Not satisfied by
systems satisfying modified forms of the Heisenberg uncertainty principle.
@ General references: Bekenstein PRD(94)gq/93;
Marolf & Roiban JHEP(04)ht [open issue];
Casini CQG(08)-a0804 [and relative entropy];
Pesci CQG(10)-a0903 [and strength of gravity, holography];
Schmitt a0901;
Bekenstein PRE(14)-a1404 [for macroscopic systems];
Longo & Xu JGP(18)-a1802 [derivation];
Page a1809-in [formulation and proof];
Bousso a1810-in [and black-hole entropy];
Buoninfante et al a2009 [generalized, with GUP];
Acquaviva et al a2011
[from fermionic fundamental constituents].
@ And cosmology: Gibbons et al PRD(06)ht [in AdS spacetime];
Haranas & Gkigkitzis MPLA(13)-a1406 [and cosmological parameters];
Banks & Fischler a1810-in.
Holographic / Covariant Bound > s.a. Relaxation
[universal bound on relaxation time]; twistors.
* Holographic bound: If A
is the area of a circumscribing surface, the entropy of a matter system
Smatter ≤ A / 4G\(\hbar\)c3 ;
This formula breaks down in large curvature/gravity situations.
* Covariant bound:
(Bousso) Formulated in terms of the fields intercepted by the ingoing
light sheet from a surface, under some assumptions and up to where the
surface has caustics, if any, as
Slight sheet ≤ A / 4G\(\hbar\)c3 .
@ General references: Bousso JHEP(99)ht,
comment Lowe JHEP(99);
Bekenstein PLB(00)ht,
ht/00-MG9 [second law];
Flanagan et al PRD(00)ht/99;
Das et al PRD(01)ht/00 [isolated horizons];
Low CQG(02)gq/01;
Casini CQG(03)gq/02 [geometric, and spacetime cutoff];
Bousso RMP(02)ht;
Mayo CQG(02);
Yurtsever PRL(03)gq [from local quantum field theory],
comment Aste ht/06;
Husain PRD(04)gq/03 [Einstein-scalar examples];
Ling & Zhang gq/06 [high-order corrections];
Pesci CQG(08)-a0803 [statistical-mechanical meaning];
Ashtekar & Wilson-Ewing PRD(08)-a0805 [and loop quantum cosmology];
Bousso et al PRD(10)-a1003 [saturation];
Van Acoleyen PRD(10)-a1009 [operational view];
Bousso PRD(16)-a1606 [asymptotic boundary version];
Hadi et al a1609 [and Padmanabhan's emergent paradigm];
Hod PRD(18)-a1806 [in higher-dimensional spacetimes];
Matsuda & Mukohyama a2007 [beyond general relativity].
@ Sufficient conditions: Bousso et al PRD(03)ht;
Gao & Lemos PRD(05)gq.
@ Applications: Danielsson JCAP(03) [inflation];
Gao & Lemos JHEP(04)ht [collapse];
Hogan ap/07 [uncertainty principle and possible measurement];
Gersl IJMPD(09)-a0804 [ideal gas of massive particles];
He & Zhang IJMPD(09)-a0805-GRF [on the dynamical horizon];
Li & Zhu CTP(12)-a1001 [dynamical horizon in lqc];
Tamaki PRD(16)-a1607 [in covariant lqg].
Cardy-Verlinde Formula > s.a. gravitational entropy.
* Idea: A holography-inspired
bound in terms of Casimir energy on field entropy in cosmology; In some limit
it can be expressed in terms of the Hubble constant.
@ General references: Verlinde ht/00;
Cai PRD(01) [Anti-de Sitter black holes];
Youm PLB(02);
Nojiri & Odintsov PLB(02) [in Yang-Mills theory];
Lin & Cai PLB(06) [re AdS black holes].
@ Corrections: Nojiri et al MPLA(01);
Momen & Sarkar PLB(02) [super-Yang-Mills];
Setare PLB(03) [topological Reissner-Nordström-de Sitter],
PRD(04)ht [from generalized uncertainty principle];
Setare IJMPA(06)gq,
IJTP(07) [non-commutativity],
IJMPA(08)-a0807 [Kerr black hole];
Darabi et al MPLA(11) [self-gravitational corrections for charged BTZ black hole].
References > s.a. laws of black-hole thermodynamics.
@ Quantum fields: Solodukhin PRD(01)gq/00 [scalar field in a cavity];
Brevik et al AP(02)
[\(\mathbb R\) × S3 geometries];
Strominger & Thompson PRD(04)ht/03 [quantum correction to the Bousso bound];
Page JHEP(08)ht/00 [non-gravitational];
Bousso et al PRD(14)-a1404 [proof of a quantum Bousso bound].
@ Charged system: Bekenstein & Mayo PRD(00)gq/99;
Hod gq/99/PRD,
PRD(00)gq/99;
Mayo PRD(99)gq;
Gour CQG(03)gq [rotating].
@ Causality-based: Brustein & Veneziano PRL(00)ht/99;
Brustein et al PLB(01) [and conformal field theory],
PRD(02) [non-singular cosmology];
Brustein LNP(08)ht/07 [and cosmology, rev].
@ Related topics: Hod PRD(00)gq/99 [rotating system];
Birmingham & Sen PRD(01)ht/00 [black holes in conformal field theory];
Gour PRD(03)gq/02 [extensive];
Elizalde & Tort PRD(03)
[massive scalar in S1 × S3];
Mignemi PRD(04)ht/03 [in 2D];
Berry & Sanders JPA(03)qp [and relationships];
Zachos JPA(07) [classical bound, including Rényi entropy];
Abreu & Visser JPCS(11)-a1011 [for uncollapsed matter],
JHEP(11)-a1012 [uncollapsed rotating bodies];
Xu & Ma MPLA(11)-a1106 [spacetime discreteness and uncertainty principle].
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