Information Theory |

**In General**
> s.a. complexity; cellular
automaton; computation; Sampling;
technology; time.

* __History__: The field was started by
Shannon in 1948; Information was identified with negative entropy by Brillouin.

* __Idea__: The justification for the
fact that information is physical comes from the relationship between information
and thermodynamics; In the theory of communications two definitions of "information"
are used; One coincides in form with the Boltzmann entropy, the other notion is
defined as the difference between unconditional and conditional entropies.

* __Remark__: If information is handled
by non-linear systems, a small noise may add no error at all.

@ __General references__: {& van der Meulen 26.03.86 mathematics talk};
Landauer PT(91)may;
news pn(97)jul;
Plenio CP(01);
Deutsch & Marletto PRS(15)-a1405 [constructor-theoretic approach];
Witten RNC(20)-a1805 [very short introduction];
Szangolies a2007-FQXi
[maximum knowledge about a system, and Bell's theorem].

@ __History__: Thomsen SHPSA(09) [re genesis of Shannon's theory].

@ __Books__: Shannon & Weaver 49;
Brillouin 56; Khinchin 57;
Billingsley 65; von Baeyer 03;
Floridi 10 [intro],
11 [philosophy].

@ __And computation__: Galindo & Martín-Delgado RMP(02)qp/01;
Buhrman et al RMP(10)-a0907 [communication complexity].

**Specific Concepts and Results**
> s.a. Meaning; Mutual Information;
quantum information; renormalization group.

* __Shannon's coding theorem__:
Establishes the amount of information that can be sent through a channel
as a function of its noise and transmission capacity.

@ __Fisher information__:
Ly et al a1705 [tutorial];
Rougerie a1912 [properties];
> s.a. quantum information;
types of action for general relativity.

@ __Information geometry__:
Rodríguez phy/98-proc;
Amari & Nagaoka 00;
Grasselli AISM(10)-mp/01 [connections];
> s.a. formulation of classical
mechanics and quantum mechanics;
metric types.

@ __And causality__: Diener PLA(96) [superluminal *v*_{g}];
Ranfagni et al PLA(06);
> s.a. causality in quantum theory [information causality].

@ __And chaos__: Touchette & Lloyd PRL(00)
+ pn(00)feb.

@ __Erasure__: Plenio & Vitelli CP(01)qp;
Vaccaro & Barnett PRS(11)-a1004 [without an energy cost];
del Rio et al Nat(11)jun
+ news pw(11)jun [cooling by erasing];
> s.a. Landauer's Principle.

@ __Quantum limits__: Bekenstein & Schiffer IJMPC(90)qp/03 [storage and transmission];
Lachmann et al AJP(04)oct-cm/99 [communication];
Lloyd et al PRL(04);
Hsu PLB(06)ht,
Yurtsever a1909 [processing];
> s.a. Holevo Bound.

@ __Information friction__:
Grover IEEE(13),
IEEE(15)-a1401 [minimum energy for communication];
Vyavahare et al CCC(14) [limits on computation].

@ __Related topics__: Chaitin IJTP(82) [Gödel's theorem],
ThSc(90)jul [ciphers];
Schumacher PRA(91) [non-separability];
in Casti 00 [Shannon theorem];
Bennett et al IEEE(14)-a0912 [reverse Shannon theorem];
Enßlin AIP(13)-a1301 [information field theory];
Kish & Granqvist IEEE(13)-a1309 [does information have mass?];
> s.a. Brudno's Theorem.

__Other aspects__: see information and physical theories;
information and spacetime / gravity; quantum information

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send feedback and suggestions to bombelli at olemiss.edu – modified 29 may 2021