Gradient and GENERIC time evolution towards reduced dynamics

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10418441" target="_blank" >RIV/00216208:11320/20:10418441 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/68407700:21340/20:00341215

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=dtydDP3JaJ" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=dtydDP3JaJ</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1098/rsta.2019.0472" target="_blank" >10.1098/rsta.2019.0472</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Gradient and GENERIC time evolution towards reduced dynamics

Popis výsledku v původním jazyce

Reduction of a mesoscopic dynamical theory to equilibrium thermodynamics brings to the latter theory the fundamental thermodynamic relation (i.e. entropy as a function of the thermodynamic state variables). The reduction is made by following the mesoscopic time evolution to its conclusion, i.e. to fixed points at which the time evolution ceases to continue. The approach to fixed points is driven by entropy, that, if evaluated at the fixed points, becomes the thermodynamic entropy. Since the fixed points are parametrized by the thermodynamic state variables (by constants of motion), the thermodynamic entropy arises as a function of the thermodynamic state variables and thus the final outcome of the reduction is the fundamental thermodynamic relation. This reduction process extends also to reductions in which the reduced theory still involves the time evolution (e.g. reduction of kinetic theory to hydrodynamics). The essence of the extension is the replacement of the mesoscopic time evolution of the state variables with the corresponding mesoscopic time evolution of the vector field (i.e. of the fluxes). The fixed point in this flux time evolution is the vector field generating the reduced mesoscopic time evolution. The flux-entropy driving the flux time evolution becomes, if evaluated at the fixed point, the flux fundamental thermodynamic relation in the reduced dynamical theory. We show that the flux-entropy is a potential related to the entropy production. This article is part of the theme issue &apos;Fundamental aspects of nonequilibrium thermodynamics&apos;.

Název v anglickém jazyce

Gradient and GENERIC time evolution towards reduced dynamics

Popis výsledku anglicky

Reduction of a mesoscopic dynamical theory to equilibrium thermodynamics brings to the latter theory the fundamental thermodynamic relation (i.e. entropy as a function of the thermodynamic state variables). The reduction is made by following the mesoscopic time evolution to its conclusion, i.e. to fixed points at which the time evolution ceases to continue. The approach to fixed points is driven by entropy, that, if evaluated at the fixed points, becomes the thermodynamic entropy. Since the fixed points are parametrized by the thermodynamic state variables (by constants of motion), the thermodynamic entropy arises as a function of the thermodynamic state variables and thus the final outcome of the reduction is the fundamental thermodynamic relation. This reduction process extends also to reductions in which the reduced theory still involves the time evolution (e.g. reduction of kinetic theory to hydrodynamics). The essence of the extension is the replacement of the mesoscopic time evolution of the state variables with the corresponding mesoscopic time evolution of the vector field (i.e. of the fluxes). The fixed point in this flux time evolution is the vector field generating the reduced mesoscopic time evolution. The flux-entropy driving the flux time evolution becomes, if evaluated at the fixed point, the flux fundamental thermodynamic relation in the reduced dynamical theory. We show that the flux-entropy is a potential related to the entropy production. This article is part of the theme issue &apos;Fundamental aspects of nonequilibrium thermodynamics&apos;.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10300 - Physical sciences

Projekt

<a href="/cs/project/GJ17-15498Y" target="_blank" >GJ17-15498Y: Víceškálová nerovnovážná termodynamika</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

ISSN

1364-503X

e-ISSN

—

Svazek periodika

378

Číslo periodika v rámci svazku

2170

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

22

Strana od-do

20190472

Kód UT WoS článku

000528728000006

EID výsledku v databázi Scopus

2-s2.0-85082565761