Arrow of Time and Irreversibility  

In General > s.a. computation; CPT symmetry [time reversal]; electromagnetism; statistical mechanics; thermodyamics; time [culturally].
* Idea: Although the fundamental laws are (apparently) time-reversible, real world processes don't seem to be; Formally described by using semigroups rather than groups of time-evolution operators in physical theories.
* Versions: Thermodynamical (the approach to equilibrium, including the tendency of potential energy to decrease, particle decay, and radiation); Quantum measurement (may not really exist); Cosmological (expansion); Gravitational (clumping); Psychological (memory of the past).
* Relationships: T Gold proposed that the thermodynamical one and the cosmological one are related; The psychological one seemed to be independent, because the entropy of the brain does not increase; 2013, Landauer's principle used to explain the relationship between psychological and thermodynamic arrows of time.
* History: 1872, Boltzmann argues that irreversibility can be derived from a time-reversible microphysics using statistical mechanics and entropy (there are logical gaps, but it has become the majority view); Eddington introduces the expression "arrow of time"; Supporters of the opinion that irreversibility is fundamental include Planck, Poincaré (statistical mechanics is primary, cannot be derived from Newtonian physics), Prigogine (the connection goes through unstable systems); 1999, Schulman's simulations, two opposite ones can coexist.
* Open future view: The common-sense view that there is an ontological difference between the past, the present, and the future; The past and the present are real, whereas the future is not yet a part of reality.
* Points of view: Irreversibility is at least partly a question of initial conditions [Boltzmann, Reichenbach, Grünbaum], but many hope there is more):
- Not fundamental: It comes from coarse-graining, disordered states being by far more numerous than ordered ones; the problem is, At what scale?
- Intermediate: Rohrlich argues that the arrow of time is not built into the fundamental equations of motion for a point particle (e.g., Lorentz-Abraham-Dirac equation), but appears in every finite-size version.
- Fundamental: Emergent structures in non-equilibrium processes, rigged Hilbert spaces (Prigogine and Brussels school), or Weyl curvature hypothesis (Penrose); The problem is, Show how.
@ I: Rothman ThSc(97)jul [Brussels school]; Magnon 97; Dodd SA(08)jan.
@ General references: Margenau PhSc(54)apr; Popper Nat(57)jun; Gold in(58), AJP(62)jun; Davies 74; Coveney Rech(89)feb; Page in(91); Price BJPS(91) [review], in(94)gq/93, 96, phy/04-proc; Mackey 92; Lebowitz PT(93)sep; Savitt ed-94, BJPS(96) [rev]; Nikolić phy/98; Rohrlich FP(98) [point particle approximation]; Bernstein & Erber JPA(99) [local vs global]; Costa de Beauregard IJTP(99); Castagnino qp/00 [global nature]; Price BJPS(02), North BJPS(02) [two conceptions]; Ćirković & Milošević-Zdjelar FS(04)phy [three]; Rovelli SHPMP(04) [refute Rohrlich]; Castagnino & Lombardi JPA(04) [non-entropic]; Zeh 07; Aiello et al FP(08) [local from global]; Feng & Crooks PRL(08) [length of time arrow]; Zeh a0908-ch [conceptual], a1012-ch [rev]; Ellis SHPMP(13)-a1302 [top-down causation]; Barbour et al a1310, PRL(14)-a1409 + new wired(14)nov [gravitational origin]; Rovelli a1407 [time-oriented coarse-graining].
@ And causality: Rohrlich SHPMP(00) [causality and self-interaction]; Nikolić FPL(06) [and causal paradoxes]; Coecke & Lal PRL(12)-a1108 [vs causal structure].
@ Psychological arrow of time: Wolpert IJTP(92), Maroney FP(10)-a0709 [and computers]; Mlodinow & Brun PRE(14)-a1310 [and the thermodynamic one].
@ Conceptual: Reichenbach 56; Rakić BJPS(97) [open future and special relativity]; Dorato SHPMP(06) [becoming]; Torretti SHPMP(07) [reexamination]; van Strien SHPMP(13) [mechanism and the reversibility objection]; Neri a1309 [meta-theoretical approach].
> Related topics: see CPT [T-reversal]; entropy; Evolution; Landauer's Principle; Recurrence; thermodynamic concepts [reversible process].

In Quantum Theory > s.a. causality and violations; locality; quantum statistical mechanics; quantum systems; resonance; time in quantum theory.
* Idea: The standard formalism rules out the existence of an arrow of time because it is based on conserved probabilities; The Brussels school proposed formalism based on the presence of resonances and the use of rigged Hilbert space and time-evolution semigroups; Or one can try quantum field theory.
@ General references: Fargue & Fer AFLB(76); Toyozawa JPSJ(89); Lenz & Życzkowski JPA(92); Page PRL(93)gq; Bohm & Kielanowski APPB(96)qp/95 [different types]; Kadomtsev SPU(95); Fain 00; D'Ariano et al PLA(00)qp [and phase squeezing]; Bishop qp/02-in; volume LNP(03)#622; de la Madrid LNP(03)qp [and boundary conditions]; Bohm IJTP(03) [resonances and decay]; Bishop IJTP(05)qp-conf [and mental systems]; Castagnino et al FP(06); Pérez-Madrid PhyA(07); Holster NJP(03) [time asymmetry]; Strauss et al a0802, comment Hall a0802 [arrow-of-time operator]; Bohm et al JPA(08)-a0803-conf; Maccone PRL(09)-a0802, comments Jennings & Rudolph PRL-a0909, Nikolić a0912, reply a0912 [resolution based on information]; David PRL(11)-a1103 [role of reversibility in the quantum formalism]; Kawamoto a1106 [analysis of microscopic reversibility]; Chiarelli a1307 [relation between micro and macro arrows of time].
@ Models: Gell-Mann & Hartle gq/93-in [and quantum cosmology]; Polonyi PRD(08)-a0801 [semiclassical Coulomb field and decoherence]; Oerter AJP(11)mar [simple model, and entropy]; Wójcik a1201 [simple model]; Hartle a1301 [in cosmology, quantum and thermodynamical and possible local arrows]; Fernández de Córdoba et al a1304 [gravitationally-induced irreversibility]; de la Torre a1411 [position-momentum correlation]; > s.a. approaches to quantum theory [sub-quantum].
@ Quantum measurement: Aharonov et al PR(64); Zeh FP(79)qp/03; Baaquie IJMPA(94) [decoherence and Friedrichs model]; Schulman 97; Bohm et al IJTP(99); Srivastava et al IJMPB(99)qp/98 [information and entropy]; Halabi NCB(10)-a0908.
@ Rigged Hilbert space: Schulte et al qp/95; Bishop IJTP(04), IJTP(05) [Bohm vs Brussels-Austin], qp/05; Bohm et al Sigma(11)-a1109 [rigged Hilbert spaces of Hardy functions]; > s.a. hilbert space.
@ Brussels school: Prigogine & Petrosky PhyA(87); Hasegawa et al FP(91); Antoniou & Prigogine PhyA(93); Bohm IJTP(97)ht [K decay]; Ordóñez PhyA(98)mp/00; Bostroem qp/00; Castagnino & Gunzig IJTP(99)qp/00 [axiomatic], qp/00 [comparison]; Bishop SHPMP(04) [overview]; Bohm et al qp/07 [framework].
@ Brussels school, critiques: Batterman PhSc(91)jun; Verstraeten PhSc(91)dec; Karakostas PhSc(96)sep.
@ In quantum field theory: Vitiello ht/01-conf; Buchholz CMP(03); Atkinson SHPMP(06) [QED]; Morgan a0810-FQXi.
@ And observation: Bohm et al qp/07 [with single ion]; > s.a. quantum effects [reversal of evolution].

Related Topics > s.a. hilbert space; measurement in quantum mechanics; time in quantum gravity.
@ Radiation: Frisch BJPS(00) [dissolution of puzzle]; Price SHPMP(06); Frisch SHPMP(06); Boozer EJP(07) [and retarded potentials].
@ In classical mechanics / thermodynamics: Schulman & Shtokhamer IJTP(77); Hutchison BJPS(93); Savitt BJPS(94); Hutchison BJPS(95) [friction implies irreversibility in practice], comment Callender BJPS(95); Zak IJTP(96); Busch CMC(00)mp/99; Zeh FPL(99)phy; Brown & Uffink SHPMP(01) [source]; Callender in(01); Muratov JPA(01) [classical statistical mechanics]; Spohn LNP(01) [hard spheres and Boltzmann equation]; Castagnino & Laciana CQG(02); Yukalov PLA(03) [quasi-isolated systems]; Winsberg PhSc(04)dec [Albert's proposal vs Reichenbach]; Tian JHEP(05)gq [thermal time, in de Sitter]; Hagar PhSc(05)jul; Maroney SHPMP(05), Gallavotti Chaos(06) [irreversibility time scale]; Ladyman et al SHPMP(07) [logical vs thermodynamical arrow of time]; Partovi PRE(08)-a0708 [violation in high-correlation environment]; Lucia PRS(08) [and ergodicity]; Swendsen AJP(08)jul [model, qualitative understanding]; Drory SHPMP(08) [no paradox]; Schulman JPCS(09)-a0811 [role of cosmology]; Trushechkin a1102 [and "functional mechanics"]; Polonyi a1206-in [environment-induced]; Jenkins AJP-a1301 [in an ideal fluid]; Muriel PLA(13) [evolution of the single-particle distribution function]; > s.a. entropy [production]; modified thermodynamics.
@ In (quantum) cosmology: Page IJTP(84) [inflation]; Hawking PRD(85); Hawking et al PRD(93)gq [from boundary conditions]; Hu in(94)gq/93 [fluctuation-dissipation relation]; Kiefer & Zeh PRD(95)gq/94 [reversal in recollapse]; Rothman & Anninos PRD(97) [clumping and phase space volume]; Dastidar MPLA(99)qp-conf [and cmb]; Allahverdyan & Gurzadyan JPA(02) [relation with thermodynamics, and cmb]; Albrecht ap/02-fs [inflation]; Castagnino et al CQG(03)qp/02, FP(03) [and other arrows]; Carroll & Chen ht/04 [spontaneous inflation]; Kiefer BJP(05)gq-proc, a0910-ch [origin is in quantum cosmology]; Wald SHPMP(06)gq/05-conf, Earman SHPMP(06) [and initial conditions]; Carroll SA(08)may; Bojowald a0910-ch [lqc]; Hartle & Hertog PRD(12)-a1106 [in the no-boundary quantum state]; Mersini-Houghton & Vaas ed-12; Gurzadyan et al a1302-conf; Ellis a1302 [and the emergent block universe]; Vilenkin PRD(13)-a1305 [and the beginning of the universe].
@ In the multiverse: Ćirković FP(03) [Boltzmann-Schütz argument]; Mersini-Houghton a0909-conf; Robles-Pérez a1203 [and entanglement].
@ And string theory: McInnes NPB(07); Bousso PRD(12)-a1112 [and the landscape, arrow of time as constraint on the vacuum structure].
@ And information: Hitchcock qp/00; Diósi LNP(04)qp/03.
@ And determinism: Elitzur & Dolev FPL(99)qp/00 [black-hole evaporation], PLA(99); Dolev et al qp/01/SHPMP.
@ And chaos: Roberts & Quispel PRP(92); Calzetta JMP(91); Lee PRL(07) [irreversibility not sufficient for chaos]; > s a. quantum chaos.
@ Opposing arrows of time: Schulman PRL(99)cm + pn(99)dec, PRL(00)cm, PLA(01)cm [causality paradoxes], comment Zeh Ent(06); Goldtein & Tumulka CQG(03) [and non-locality]; Kupervasser et al FP(12)-a1011, Kupervasser a1106 [instability and universal arrow of time].
@ Versions, examples: Baker AJP(86)aug [simple model]; Géhéniau & Prigogine FP(86); Bonnor PLA(85), PLA(87) [gravitational]; Brout FP(87); Brout et al PLB(87); Fukuyama & Morikawa PRD(89); Kupervasser EJTP-a1107; > s.a. Coarse-Graining.
@ Numerical experiments: Fowles AJP(94)apr; Georgeot & Shepelyansky EPJD(02)qp/01 [and quantum computers].

"Then go and invert them" - Boltzmann to Loschmidt, who had asked him what
happens to his statistical theory if one inverts the velocities of all particles.

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