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-a1409 [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; 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]; > 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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send feedback and suggestions to bombelli at olemiss.edu – modified 11
sep
2014