Information Theory

In General > s.a. complexity; Cellular Automaton; computation; Sampling; technology; time.
* History: 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).
@ Books: Shannon & Weaver 49; Brillouin 56; Khinchin 57; Billingsley 65; von Baeyer 03.
@ And computation: Kak FP(96) [and physics]; Galindo & Martín-Delgado RMP(02)qp/01.

Specific Concepts and Results > s.a. quantum information.
* 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.
* Mutual information: In general, a quantity that quantifies the determinism that exists in a relationship between random variables; For disjoint spacetime regions V and W, I(V,W):= S(V) + S(W) – S(V W); A measure of the shared information or correlation between the two regions; Satisfies the inequality I(V,W) 2 min(S(V), S(W)), and can be thought of as a "point-splitting" regularization of the entropy.
@ Information geometry: Rodríguez phy/98; Grasselli mp/01 [connections]; > s.a. metric types.
@ And causality: Diener PLA(96) [superluminal v_g]; Ranfagni et al PLA(06).
@ And chaos: Touchette & Lloyd PRL(00) + pn(00)feb.
@ Mutual information: Casini CQG(07)gq/06; Evans PRS(08) [computationally efficient estimator].
@ Quantum limits: Bekenstein & Schiffer IJMPC(90)qp/03 [storage and transmission]; Lachmann et al AJP(04)cm/99 [communication]; Lloyd et al PRL(04); Hsu PLB(06)ht [processing].
@ Related topics: Chaitin IJTP(82) [Gödel's theorem]; ThSc(90)jul, 52-54 [ciphers]; Schumacher PRA(91) [non-separability]; in Casti 00 [Shannon theorem]; Plenio & Vitelli CP(01)qp [erasure]; > Brudno's Theorem, Landauer's Principle.

And Physical Theories > s.a. critical phenomena; entropy; physics; statistical mechanics and states.
* History: 1990, Wheeler launched his "it from bit" project to try and derive physics from information theory.
@ General references: Hartle PRD(95)gq/94, comment Kent PRD(97)gq/96 [and decoherent histories]; Grandy AJP(97)RL; Pospiech qp/00/EJP [intro, quantum mechanics]; Semitecolos qp/02; Faigon qp/03, Busch qp/04-in [classical and quantum mechanics]; Adami qp/04, Gisin qp/04 [rev]; Plastino PhyA(04) [Wheeler's "it from bit"], PhyA(04) [statistical mechanics and thermodynamics]; Halvorson SHPMP(04) [characterization of theories]; Bais & Farmer a0708-in [rev]; Caticha a0710-in [and entropy]; Paterek et al a0804 [quantum mechanics and other possible theories].
@ Fisher information: Lavis & Streater SHPMP(02); Nettleton JPA(03) [and entropy]; Pennini & Plastino PLA(06) [and canonical ensemble]; Gibilisco et al a0712 [and quantum covariance].
@ Thermodynamics: Fort CP(99) [non-equilibrium matter + radiation]; > s.a. Open System.
@ And gravity: Bekenstein SHPMP(01) [black holes]; > s.a. black holes and information, quantum black holes.
@ And holography: Correa-Borbonet IJQI(05)ht/04 [Shannon & Boltzmann entropies]; Wolf et al a0704 [thermal equilibrium, area scaling of information and correlations].

And Spacetime / Gravity > s.a. quantum spacetime; spacetime [measurement].
* And spacetime: Hints of a limit to how much information can be stored in a spacetime region come from the holographic bound.
@ Spacetime: Harmuth 93; Cocke & Frieden FP(97); Frieden 98 [Fisher info]; Volovich qp/01; Lloyd PRL(02)qp/01; Bekenstein qp/01-in, qp/01-in; Terno qp/01-in [curved spacetime]; Volovich qp/02, qp/02-in; Peres & Terno RMP(04)qp/02 [overview]; Garisto qp/02 [speed]; Kempf PRL(04)gq/03, gq/03-in [sampling, covariant]; Ng & van Dam IJMPA(05)gq/04-in [black hole quantum computers]; Kribs & Markopoulou gq/05 [emergence of geometry]; Hsu IJMPA(07)-a0704; Kempf & Martin PRL(08) [and spectral geometry].
@ Sampling and discreteness: Kempf gq/04-in.
@ Cosmology: Tegmark FPL(96)qp [little information, complicated dynamics]; Hogan ap/02-in [inflation]; Barrow & Hervik PLB(03) [open universes]; Hosoya et al PRL(04) [inhomogeneous]; Gough a0709 [information equation of state]; > s.a. anthropic principle.

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Send feedback and suggestions to bombelli at olemiss.edu – Modified 21 jun 2008