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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Journal of Mathematical Physics

ISSN

0022-2488

e-ISSN

1089-7658

Svazek periodika

63

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

22

Strana od-do

123305

Kód UT WoS článku

000898206300004

EID výsledku v databázi Scopus

2-s2.0-85144364106