<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-03457502</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-16T16:43:09+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Quantifying Non-Stationarity with Information Theory</title>
            <author role="aut">
              <persName>
                <forename type="first">Carlos</forename>
                <surname>Granero-Belinchon</surname>
              </persName>
              <email type="md5">024112d073f033e5cb214d245b50e171</email>
              <email type="domain">imt-atlantique.fr</email>
              <idno type="idhal" notation="string">carlos-granero-belinchon</idno>
              <idno type="idhal" notation="numeric">737486</idno>
              <idno type="halauthorid" notation="string">30762-737486</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-4095-0807</idno>
              <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=vKwDG3kAAAAJ&amp;hl=fr</idno>
              <orgName ref="#struct-481355"/>
              <affiliation ref="#struct-1067634"/>
              <affiliation ref="#struct-1060206"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Stéphane G.</forename>
                <surname>Roux</surname>
              </persName>
              <email type="md5">e48480b16034df94516b44b5c573ca7c</email>
              <email type="domain">ens-lyon.fr</email>
              <idno type="idhal" notation="string">stephane-gaetan-roux</idno>
              <idno type="idhal" notation="numeric">179555</idno>
              <idno type="halauthorid" notation="string">29445-179555</idno>
              <idno type="ORCID">https://orcid.org/0000-0001-8561-1270</idno>
              <idno type="IDREF">https://www.idref.fr/14772984X</idno>
              <affiliation ref="#struct-1166986"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Nicolas</forename>
                <surname>B. Garnier</surname>
              </persName>
              <email type="md5">3fb5cfee455c24019c4c78336729d58e</email>
              <email type="domain">ens-lyon.fr</email>
              <idno type="idhal" notation="string">nicolas-garnier</idno>
              <idno type="idhal" notation="numeric">16207</idno>
              <idno type="halauthorid" notation="string">1740-16207</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-1094-7201</idno>
              <idno type="ARXIV">https://arxiv.org/a/garnier_n_1</idno>
              <idno type="RESEARCHERID">http://www.researcherid.com/rid/H-4439-2012</idno>
              <idno type="IDREF">https://www.idref.fr/166371548</idno>
              <affiliation ref="#struct-1166986"/>
              <affiliation ref="#struct-441569"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Nicolas</forename>
                <surname>Garnier</surname>
              </persName>
              <email type="md5">3fb5cfee455c24019c4c78336729d58e</email>
              <email type="domain">ens-lyon.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2021-11-30 16:14:35</date>
              <date type="whenModified">2026-01-23 09:12:07</date>
              <date type="whenReleased">2021-12-01 08:40:14</date>
              <date type="whenProduced">2021-11-30</date>
              <date type="whenEndEmbargoed">2021-11-30</date>
              <ref type="file" target="https://hal.science/hal-03457502v1/document">
                <date notBefore="2021-11-30"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-03457502v1/file/entropy-1468345-2021-11-29.pdf" id="file-3457502-3034365">
                <date notBefore="2021-11-30"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/2112.00325"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="101257">
                <persName>
                  <forename>Nicolas</forename>
                  <surname>Garnier</surname>
                </persName>
                <email type="md5">3fb5cfee455c24019c4c78336729d58e</email>
                <email type="domain">ens-lyon.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-03457502</idno>
            <idno type="halUri">https://hal.science/hal-03457502</idno>
            <idno type="halBibtex">granerobelinchon:hal-03457502</idno>
            <idno type="halRefHtml">&lt;i&gt;Entropy&lt;/i&gt;, 2021, &lt;a target="_blank" href="https://dx.doi.org/10.3390/e23121609"&gt;&amp;#x27E8;10.3390/e23121609&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Entropy, 2021, &amp;#x27E8;10.3390/e23121609&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://creativecommons.org/licenses/by/4.0/">CC BY 4.0 - Attribution<ref corresp="#file-3457502-3034365"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="ENS-LYON">École Normale Supérieure de Lyon</idno>
            <idno type="stamp" n="UNIV-BREST">Université de Bretagne occidentale - Brest (UBO)</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-UBS">Université de Bretagne Sud</idno>
            <idno type="stamp" n="LAB-STICC_UBO" corresp="UNIV-BREST">Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance, site de l'UBO</idno>
            <idno type="stamp" n="ENIB">Ecole Nationale d'Ingénieurs de Brest</idno>
            <idno type="stamp" n="LAB-STICC">Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance</idno>
            <idno type="stamp" n="LAB-STICC_IMTA">Lab-STICC - IMT Atlantique</idno>
            <idno type="stamp" n="IMT-ATLANTIQUE" corresp="INSTITUT-MINES-TELECOM">IMT-ATLANTIQUE</idno>
            <idno type="stamp" n="PRACOM">Chaire Pracom</idno>
            <idno type="stamp" n="UDL">UDL</idno>
            <idno type="stamp" n="UNIV-LYON">Université de Lyon</idno>
            <idno type="stamp" n="INSTITUTS-TELECOM">composantes instituts telecom </idno>
            <idno type="stamp" n="TEST-HALCNRS">Collection test HAL CNRS</idno>
            <idno type="stamp" n="IMTA_MEE">IMT Atlantique - Département mathematical and electrical engineering</idno>
            <idno type="stamp" n="LAB-STICC_OSE_IMTA" corresp="IMT-ATLANTIQUE">OSE - Observations Signal &amp; Environnement (Lab-STICC)</idno>
            <idno type="stamp" n="LAB-STICC_OSE">Equipe Observations Signal &amp; Environnement</idno>
            <idno type="stamp" n="LAB-STICC_IAOCEAN">Pôle AI &amp; Ocean</idno>
            <idno type="stamp" n="INSTITUT-MINES-TELECOM">Institut Mines Telecom</idno>
            <idno type="stamp" n="LPENSL">Laboratoire de physique de l'ENS de Lyon</idno>
            <idno type="stamp" n="IP-PARIS-INFORMATION-COMMUNICATION-ELECTRONIQUE">IP Paris Département d'Information, de Communication et d'Électronique</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Quantifying Non-Stationarity with Information Theory</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Carlos</forename>
                    <surname>Granero-Belinchon</surname>
                  </persName>
                  <email type="md5">024112d073f033e5cb214d245b50e171</email>
                  <email type="domain">imt-atlantique.fr</email>
                  <idno type="idhal" notation="string">carlos-granero-belinchon</idno>
                  <idno type="idhal" notation="numeric">737486</idno>
                  <idno type="halauthorid" notation="string">30762-737486</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-4095-0807</idno>
                  <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=vKwDG3kAAAAJ&amp;hl=fr</idno>
                  <orgName ref="#struct-481355"/>
                  <affiliation ref="#struct-1067634"/>
                  <affiliation ref="#struct-1060206"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Stéphane G.</forename>
                    <surname>Roux</surname>
                  </persName>
                  <email type="md5">e48480b16034df94516b44b5c573ca7c</email>
                  <email type="domain">ens-lyon.fr</email>
                  <idno type="idhal" notation="string">stephane-gaetan-roux</idno>
                  <idno type="idhal" notation="numeric">179555</idno>
                  <idno type="halauthorid" notation="string">29445-179555</idno>
                  <idno type="ORCID">https://orcid.org/0000-0001-8561-1270</idno>
                  <idno type="IDREF">https://www.idref.fr/14772984X</idno>
                  <affiliation ref="#struct-1166986"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Nicolas</forename>
                    <surname>B. Garnier</surname>
                  </persName>
                  <email type="md5">3fb5cfee455c24019c4c78336729d58e</email>
                  <email type="domain">ens-lyon.fr</email>
                  <idno type="idhal" notation="string">nicolas-garnier</idno>
                  <idno type="idhal" notation="numeric">16207</idno>
                  <idno type="halauthorid" notation="string">1740-16207</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-1094-7201</idno>
                  <idno type="ARXIV">https://arxiv.org/a/garnier_n_1</idno>
                  <idno type="RESEARCHERID">http://www.researcherid.com/rid/H-4439-2012</idno>
                  <idno type="IDREF">https://www.idref.fr/166371548</idno>
                  <affiliation ref="#struct-1166986"/>
                  <affiliation ref="#struct-441569"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">801</idno>
                <idno type="eissn">1099-4300</idno>
                <title level="j">Entropy</title>
                <imprint>
                  <publisher>MDPI</publisher>
                  <date type="datePub">2021-11-30</date>
                </imprint>
              </monogr>
              <idno type="arxiv">2112.00325</idno>
              <idno type="doi">10.3390/e23121609</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">entropy</term>
                <term xml:lang="en">entropy-rate</term>
                <term xml:lang="en">non-stationarity</term>
                <term xml:lang="en">regularity</term>
                <term xml:lang="en">fluid turbulence</term>
              </keywords>
              <classCode scheme="halDomain" n="phys.phys.phys-data-an">Physics [physics]/Physics [physics]/Data Analysis, Statistics and Probability [physics.data-an]</classCode>
              <classCode scheme="halDomain" n="phys.phys.phys-flu-dyn">Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We introduce an index based on information theory to quantify the stationarity of a stochastic process.The index compares on the one hand the information contained in the increment at the time scale $\tau$ of the process at time $t$ with, on the other hand, the extra information in the variable at time $t$ that is not present at time $t-\tau$. By varying the scale $\tau$, the index can explore a full range of scales. We thus obtain a multi-scale quantity that is not restricted to the first two moments of the density distribution, nor to the covariance, but that probes the complete dependences in the process. This index indeed provides a measure of the regularity of the process at a given scale.Not only is this index  able to indicate whether a realization of the process is stationary, but its evolution across scales also indicates how rough and non-stationary it is.We show how the index behaves for various synthetic processes proposed to model fluid turbulence, as well as on experimental fluid turbulence measurements.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-1067634" status="OLD">
          <orgName>Equipe Observations Signal &amp; Environnement</orgName>
          <orgName type="acronym">Lab-STICC_OSE</orgName>
          <date type="start">2021-01-01</date>
          <date type="end">2024-12-31</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation name="UMR6285" active="#struct-486345" type="direct"/>
            <relation active="#struct-131284" type="indirect"/>
            <relation active="#struct-300314" type="indirect"/>
            <relation active="#struct-1705235" type="indirect"/>
            <relation active="#struct-172265" type="indirect"/>
            <relation active="#struct-301846" type="indirect"/>
            <relation active="#struct-302102" type="indirect"/>
            <relation name="UMR6285" active="#struct-441569" type="indirect"/>
            <relation active="#struct-469973" type="indirect"/>
            <relation active="#struct-481355" type="indirect"/>
          </listRelation>
        </org>
        <org type="department" xml:id="struct-1060206" status="VALID">
          <orgName>Département Mathematical and Electrical Engineering</orgName>
          <orgName type="acronym">IMT Atlantique - MEE</orgName>
          <date type="start">2021-01-01</date>
          <desc>
            <address>
              <addrLine>IMT Atlantique - Campus de Brest - Technopôle Brest-Iroise CS 8381829238 BREST Cedex 3</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-481355" type="direct"/>
            <relation active="#struct-302102" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-1166986" status="VALID">
          <idno type="IdRef">182438627</idno>
          <idno type="ISNI">0000000403847821</idno>
          <idno type="RNSR">199812078S</idno>
          <idno type="ROR">https://ror.org/00w5ay796</idno>
          <idno type="Wikidata">Q30261507</idno>
          <orgName>Laboratoire de Physique de l'ENS Lyon</orgName>
          <orgName type="acronym">Phys-ENS</orgName>
          <date type="start">2021-01-01</date>
          <desc>
            <address>
              <addrLine>46 allée d'Italie 69007 Lyon</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ens-lyon.fr/PHYSIQUE/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-6818" type="direct"/>
            <relation active="#struct-301088" type="direct"/>
            <relation name="UMR5672" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-486345" status="OLD">
          <idno type="IdRef">167731432</idno>
          <idno type="RNSR">201220091R</idno>
          <idno type="ROR">https://ror.org/0266kfd37</idno>
          <orgName>Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance</orgName>
          <orgName type="acronym">Lab-STICC</orgName>
          <date type="start">2008-01-01</date>
          <date type="end">2024-12-31</date>
          <desc>
            <address>
              <addrLine>Technopole Brest Iroise CS 83818 29238 BREST cedex 3</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://labsticc.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-131284" type="direct"/>
            <relation active="#struct-300314" type="direct"/>
            <relation active="#struct-1705235" type="indirect"/>
            <relation active="#struct-172265" type="direct"/>
            <relation active="#struct-301846" type="direct"/>
            <relation active="#struct-302102" type="direct"/>
            <relation name="UMR6285" active="#struct-441569" type="direct"/>
            <relation active="#struct-469973" type="direct"/>
            <relation active="#struct-481355" type="direct"/>
          </listRelation>
        </org>
        <org type="regrouplaboratory" xml:id="struct-131284" status="VALID">
          <idno type="ROR">https://ror.org/02ypw0a72</idno>
          <orgName>École Nationale d'Ingénieurs de Brest</orgName>
          <orgName type="acronym">ENIB</orgName>
          <desc>
            <address>
              <addrLine>945 avenue du Technopole - 29280 Plouzané</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.enib.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300314" type="direct"/>
            <relation active="#struct-1705235" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-300314" status="VALID">
          <idno type="IdRef">291809022</idno>
          <idno type="ISNI">0000000121880893</idno>
          <idno type="ROR">https://ror.org/0372th171</idno>
          <orgName>Université de Brest</orgName>
          <orgName type="acronym">UBO EPE</orgName>
          <desc>
            <address>
              <addrLine>Université de Bretagne Occidentale - 3 Rue des Archives 29238, Brest</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-brest.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-1705235" status="VALID">
          <idno type="IdRef">291816037</idno>
          <orgName>Institut National Polytechnique de Bretagne</orgName>
          <orgName type="acronym">Bretagne INP</orgName>
          <date type="start">2025-03-01</date>
          <desc>
            <address>
              <addrLine>945 avenue du Technopôle Brest-Iroise, 29289 Plouzané</addrLine>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-172265" status="VALID">
          <idno type="IdRef">05017746X</idno>
          <idno type="ISNI">0000000121680285</idno>
          <idno type="ROR">https://ror.org/04ed7fw48</idno>
          <orgName>Université de Bretagne Sud</orgName>
          <orgName type="acronym">UBS</orgName>
          <date type="start">1995-02-07</date>
          <desc>
            <address>
              <addrLine>BP 92116 - 56321 Lorient cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-ubs.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-301846" status="OLD">
          <idno type="IdRef">177263660</idno>
          <idno type="ROR">https://ror.org/059n54003</idno>
          <orgName>École Nationale Supérieure de Techniques Avancées Bretagne</orgName>
          <orgName type="acronym">ENSTA Bretagne</orgName>
          <date type="end">2024-12-31</date>
          <desc>
            <address>
              <addrLine>2 rue François Verny, 29806 Brest cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ensta-bretagne.fr</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-302102" status="VALID">
          <idno type="IdRef">192427156</idno>
          <idno type="ISNI">000000012202567X</idno>
          <idno type="ROR">https://ror.org/025vp2923</idno>
          <idno type="Wikidata">Q27962533</idno>
          <orgName>Institut Mines-Télécom [Paris]</orgName>
          <orgName type="acronym">IMT</orgName>
          <date type="start">2012-03-01</date>
          <desc>
            <address>
              <addrLine>19 Place Marguerite Perey, 91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.imt.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-469973" status="VALID">
          <idno type="IdRef">191639044</idno>
          <idno type="ROR">https://ror.org/04x1a4s97</idno>
          <orgName>Université Bretagne Loire</orgName>
          <orgName type="acronym">UBL</orgName>
          <date type="start">2016-04-01</date>
          <desc>
            <address>
              <addrLine>Cité Internationale, 1 place Paul Ricoeur - CS 54417 35044 RENNES CEDEX</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://u-bretagneloire.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-481355" status="VALID">
          <idno type="IdRef">202743233</idno>
          <idno type="ROR">https://ror.org/030hj3061</idno>
          <orgName>IMT Atlantique</orgName>
          <orgName type="acronym">IMT Atlantique</orgName>
          <date type="start">2017-01-01</date>
          <desc>
            <address>
              <addrLine>Campus Brest : Technopôle Brest-Iroise CS 8381829238 BREST Cedex 3 -Campus Nantes : 4, rue Alfred Kastler- La chantrerie 44300 NANTES -Campus Rennes :  2 Rue de la Châtaigneraie, 35510 CESSON SEVIGNE</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.imt-atlantique.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-302102" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-6818" status="VALID">
          <idno type="IdRef">149154992</idno>
          <idno type="ISNI">0000000123319856</idno>
          <idno type="ROR">https://ror.org/04zmssz18</idno>
          <idno type="Wikidata">Q10159</idno>
          <orgName>École normale supérieure de Lyon</orgName>
          <orgName type="acronym">ENS de Lyon</orgName>
          <date type="start">2010-01-01</date>
          <desc>
            <address>
              <addrLine>15 parvis René Descartes - BP 7000 - 69342 Lyon Cedex 07</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ens-lyon.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301088" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-301088" status="VALID">
          <idno type="ROR">https://ror.org/01rk35k63</idno>
          <orgName>Université de Lyon</orgName>
          <desc>
            <address>
              <addrLine>92 rue Pasteur - CS 30122, 69361 Lyon Cedex 07</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.universite-lyon.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>