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On the role of geometry in statistical mechanics and thermodynamics. II. Thermodynamic perspective

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10453036" target="_blank" >RIV/00216208:11320/22:10453036 - isvavai.cz</a>

  • Result on the web

    <a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=oPzxZGScXf" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=oPzxZGScXf</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1063/5.0099930" target="_blank" >10.1063/5.0099930</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    On the role of geometry in statistical mechanics and thermodynamics. II. Thermodynamic perspective

  • Original language description

    The General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) provides the structure of mesoscopic multiscale dynamics that guarantees the emergence of equilibrium states. Similarly, a lift of the GENERIC structure to iterated cotangent bundles, called a rate GENERIC, guarantees the emergence of the vector fields that generate the approach to equilibrium. Moreover, the rate GENERIC structure also extends Onsager&apos;s variational principle. The maximum entropy principle in the GENERIC structure becomes the Onsager variational principle in the rate GENERIC structure. In the absence of external forces, the rate entropy is a potential that is closely related to the entropy production. In the presence of external forces when the entropy does not exist, the rate entropy still exists. While the entropy at the conclusion of the GENERIC time evolution gives rise to equilibrium thermodynamics, the rate entropy at the conclusion of the rate GENERIC time evolution gives rise to rate thermodynamics. Both GENERIC and rate GENERIC structures are put into the geometrical framework in the first paper of this series. The rate GENERIC is also shown to be related to Grad&apos;s hierarchy analysis of reductions of the Boltzmann equation. Chemical kinetics and kinetic theory provide illustrative examples. We introduce rate GENERIC extensions (and thus also Onsager-variational-principle formulations) of both chemical kinetics and the Boltzmann kinetic theory. Published under an exclusive license by AIP Publishing.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10102 - Applied mathematics

Result continuities

  • Project

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2022

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Journal of Mathematical Physics

  • ISSN

    0022-2488

  • e-ISSN

    1089-7658

  • Volume of the periodical

    63

  • Issue of the periodical within the volume

    12

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    22

  • Pages from-to

    123305

  • UT code for WoS article

    000898206300004

  • EID of the result in the Scopus database

    2-s2.0-85144364106