Information
Theory |

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

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

* __Idea__: 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].

@ __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.

@ __Information geometry__: Rodríguez phy/98-proc;
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
[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 24 jul
2017