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 vg]; 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.

blue bullet Other aspects: see information and physical theories; information and spacetime / gravity; quantum information


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