Arrow of Time and Irreversibility  

In General > s.a. computation; 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 entropy production and 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 and cosmological ones 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); 1927, 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, a1505 [time-oriented coarse-graining].
@ 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].
> Online resources: see Wikipedia page; 2015 video with interviews.
blue bullet Related subjects: see arrow of time in various physical theories.

Related Topics > s.a. CPT symmetry [time reversal]; hilbert space; measurement in quantum mechanics; time in quantum gravity.
@ And causality: Rohrlich SHPMP(00) [causality and self-interaction]; Nikolić FPL(06) [and causal paradoxes]; Coecke & Lal PRL(12)-a1108 [vs causal 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 EJTP-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].
> Related topics: see CPT [T-reversal]; entropy; Evolution; Landauer's Principle; Recurrence; thermodynamic concepts [reversible process].

"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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