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 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); 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].

__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 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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send feedback and suggestions to bombelli at olemiss.edu – modified 7
jun
2015