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'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'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
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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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