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  <doc>
    <id>8019</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>13</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>46</volume>
    <type>article</type>
    <publisherName>De Gruyter</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2021-01-01</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Framework of Nonequilibrium Statistical Mechanics. I. Role and Types of Fluctuations</title>
    <abstract language="eng">Understanding the fluctuations by which phenomenological evolution equations with thermodynamic structure can be enhanced is the key to a general framework of nonequilibrium statistical mechanics. These fluctuations provide an idealized representation of microscopic details. We consider fluctuation-enhanced equations associated with Markov processes and elaborate the general recipes for evaluating dynamic material properties, which characterize force-flux constitutive laws, by statistical mechanics. Markov processes with continuous trajectories are conveniently characterized by stochastic differential equations and lead to Green–Kubo-type formulas for dynamic material properties. Markov processes with discontinuous jumps include transitions over energy barriers with the rates calculated by Kramers. We describe a unified approach to Markovian fluctuations and demonstrate how the appropriate type of fluctuations (continuous versus discontinuous) is reflected in the mathematical structure of the phenomenological equations.</abstract>
    <parentTitle language="eng">Journal of Non-Equilibrium Thermodynamics</parentTitle>
    <identifier type="doi">10.1515/jnet-2020-0068</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2020-08-13</enrichment>
    <author>Hans Christian Öttinger</author>
    <submitter>Alberto Montefusco</submitter>
    <author>Alberto Montefusco</author>
    <author>Mark A. Peletier</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="projects" number="SFB1114-C3">SFB1114-C3</collection>
    <collection role="institutes" number="MfLMS">Mathematics for Life and Materials Science</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
  <doc>
    <id>8020</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>15</pageFirst>
    <pageLast>33</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>46</volume>
    <type>article</type>
    <publisherName>De Gruyter</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2021-01-01</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Framework of Nonequilibrium Statistical Mechanics. II. Coarse-Graining</title>
    <abstract language="eng">For a given thermodynamic system, and a given choice of coarse-grained state variables, the knowledge of a force-flux constitutive law is the basis for any nonequilibrium modeling. In the first paper of this series we established how, by a generalization of the classical fluctuation-dissipation theorem (FDT), the structure of a constitutive law is directly related to the distribution of the fluctuations of the state variables. When these fluctuations can be expressed in terms of diffusion processes, one may use Green–Kubo-type coarse-graining schemes to find the constitutive laws. In this paper we propose a coarse-graining method that is valid when the fluctuations are described by means of general Markov processes, which include diffusions as a special case. We prove the success of the method by numerically computing the constitutive law for a simple chemical reaction A⇄B. Furthermore, we show that, for such a system, one cannot find a consistent constitutive law by any Green–Kubo-like scheme.</abstract>
    <parentTitle language="eng">Journal of Non-Equilibrium Thermodynamics</parentTitle>
    <identifier type="doi">10.1515/jnet-2020-0069</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2020-09-14</enrichment>
    <author>Alberto Montefusco</author>
    <submitter>Alberto Montefusco</submitter>
    <author>Mark A. Peletier</author>
    <author>Hans Christian Öttinger</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="projects" number="SFB1114-C3">SFB1114-C3</collection>
    <collection role="institutes" number="MfLMS">Mathematics for Life and Materials Science</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
  </doc>
</export-example>
