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).
@ History: Thomsen SHPSA(09) [re genesis of Shannon’s theory].
@ 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; Buhrman et al RMP-a0907 [communication complexity]; Mézard & Montanari 09 [and physics].

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. formulation of classical mechanics, metric types.
@ And causality: Diener PLA(96) [superluminal vg]; 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)oct-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.
* Statistical mechanics and thermodynamics: The Khinchin axioms fix the most desirable properties an information measure should have, and ultimately lead to the Shannon entropy as the fundamental information measure on which statistical mechanics is based.
@ General references: Hartle PRD(95)gq/94, comment Kent PRD(97)gq/96 [and decoherent histories]; Grandy AJP(97)jun-RL; Pospiech qp/00/EJP [intro, quantum mechanics]; Semitecolos qp/02-wd; 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"]; Halvorson SHPMP(04) [characterization of theories]; Bais & Farmer a0708-in [rev]; Paterek et al a0804 [quantum mechanics and other possible theories]; Karnani et al PRS(09); Ng & Parwani a0908 [relativistic quantum spinors].
@ 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].
@ Statistical mechanics and thermodynamics: Fort CP(99) [non-equilibrium matter + radiation]; Plastino PhyA(04); Caticha a0710-in [and entropy]; Beck CP(09) [generalized measures, and entropy]; Dahlsten et al a0908 [work value]; Short & Wehner a0909 [and entropy]; Ellison et al JSP(09) [amount of information stored in the present]; > 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 PRL(08)-a0704 [thermal equilibrium, area scaling of information and correlations].

And Spacetime / Gravity > s.a. computation [the universe as a computer]; 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)-a0708 [and spectral geometry]; Oppenheim & Reznik a0902 [relational theory of information destruction, and conservation laws].
@ 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 Ent(08)-a0709 [information equation of state]; > s.a. anthropic principle.

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