Time arrow without past hypothesis: a toy model explanation

The laws of Physics are time-reversible, making no qualitative distinction between the past and the future—yet we can only go towards the future. This apparent contradiction is known as the ‘arrow of time problem’. Its current resolution states that the future is the direction of increasing entropy....

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Main Authors: Pablo Arrighi, Gilles Dowek, Amélia Durbec
Format: Article
Language:English
Published: IOP Publishing 2024-01-01
Series:New Journal of Physics
Subjects:
Online Access:https://doi.org/10.1088/1367-2630/ad93f5
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author Pablo Arrighi
Gilles Dowek
Amélia Durbec
author_facet Pablo Arrighi
Gilles Dowek
Amélia Durbec
author_sort Pablo Arrighi
collection DOAJ
description The laws of Physics are time-reversible, making no qualitative distinction between the past and the future—yet we can only go towards the future. This apparent contradiction is known as the ‘arrow of time problem’. Its current resolution states that the future is the direction of increasing entropy. But entropy can only increase towards the future if it was low in the past, and past low entropy is a very strong assumption to make, because low entropy states are rather improbable, non-generic. Recent works from the Physics literature suggest, however, we may do away with this so-called ‘past hypothesis’, in the presence of reversible dynamical laws featuring expansion. We prove that this can be the case in principle, within a toy model. It consists in graphs upon which particles circulate and interact according to local reversible rules. Some rules locally shrink or expand the graph. We prove that almost all states expand; entropy always increases as a consequence of expansion—thereby providing a local explanation for the rise of an entropic arrow of time without the need for a past hypothesis. The discrete setting of this toy model allows us to deploy the full rigour of theoretical Computer Science proof techniques. It also allows for the numerical exploration of several physically-motivated variants: a time-symmetric variant; two inflationary variants; and a damping variant—which slows down thermal death. The fact that all of these models exhibit similar behaviours suggests that local reversible expansion mechanisms constitute a robust recipe for a time arrow without past hypothesis. In this qualitative sense, the explanation may therefore also be relevant at the cosmological level.
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spelling doaj-art-d550a5957baa4e008e7647331b6948b12024-11-28T11:47:10ZengIOP PublishingNew Journal of Physics1367-26302024-01-01261111301910.1088/1367-2630/ad93f5Time arrow without past hypothesis: a toy model explanationPablo Arrighi0https://orcid.org/0000-0002-3535-1009Gilles Dowek1Amélia Durbec2https://orcid.org/0000-0002-3464-4440Université Paris-Saclay , Inria, CNRS, LMF, 91190 Gif-sur-Yvette, FranceUniversité Paris-Saclay , Inria, CNRS, LMF, 91190 Gif-sur-Yvette, FranceCNRS , Centrale Lille, JUNIA, Univ. Lille, Univ. Valenciennes, UMR 8520 IEMN, 59046 Lille Cedex, FranceThe laws of Physics are time-reversible, making no qualitative distinction between the past and the future—yet we can only go towards the future. This apparent contradiction is known as the ‘arrow of time problem’. Its current resolution states that the future is the direction of increasing entropy. But entropy can only increase towards the future if it was low in the past, and past low entropy is a very strong assumption to make, because low entropy states are rather improbable, non-generic. Recent works from the Physics literature suggest, however, we may do away with this so-called ‘past hypothesis’, in the presence of reversible dynamical laws featuring expansion. We prove that this can be the case in principle, within a toy model. It consists in graphs upon which particles circulate and interact according to local reversible rules. Some rules locally shrink or expand the graph. We prove that almost all states expand; entropy always increases as a consequence of expansion—thereby providing a local explanation for the rise of an entropic arrow of time without the need for a past hypothesis. The discrete setting of this toy model allows us to deploy the full rigour of theoretical Computer Science proof techniques. It also allows for the numerical exploration of several physically-motivated variants: a time-symmetric variant; two inflationary variants; and a damping variant—which slows down thermal death. The fact that all of these models exhibit similar behaviours suggests that local reversible expansion mechanisms constitute a robust recipe for a time arrow without past hypothesis. In this qualitative sense, the explanation may therefore also be relevant at the cosmological level.https://doi.org/10.1088/1367-2630/ad93f5lattice gas automatanetworks dynamicsentropy
spellingShingle Pablo Arrighi
Gilles Dowek
Amélia Durbec
Time arrow without past hypothesis: a toy model explanation
New Journal of Physics
lattice gas automata
networks dynamics
entropy
title Time arrow without past hypothesis: a toy model explanation
title_full Time arrow without past hypothesis: a toy model explanation
title_fullStr Time arrow without past hypothesis: a toy model explanation
title_full_unstemmed Time arrow without past hypothesis: a toy model explanation
title_short Time arrow without past hypothesis: a toy model explanation
title_sort time arrow without past hypothesis a toy model explanation
topic lattice gas automata
networks dynamics
entropy
url https://doi.org/10.1088/1367-2630/ad93f5
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AT gillesdowek timearrowwithoutpasthypothesisatoymodelexplanation
AT ameliadurbec timearrowwithoutpasthypothesisatoymodelexplanation