On the role of geometry in statistical mechanics and thermodynamics. I. Geometric perspective
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10453035" target="_blank" >RIV/00216208:11320/22:10453035 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=o2YDhrVttC" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=o2YDhrVttC</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/5.0099923" target="_blank" >10.1063/5.0099923</a>
Alternative languages
Result language
angličtina
Original language name
On the role of geometry in statistical mechanics and thermodynamics. I. Geometric perspective
Original language description
This paper contains a fully geometric formulation of the General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC). Although GENERIC, which is the sum of Hamiltonian mechanics and gradient dynamics, is a framework unifying a vast range of models in non-equilibrium thermodynamics, it has unclear geometric structure due to the diverse geometric origins of Hamiltonian mechanics and gradient dynamics. The difference can be overcome by cotangent lifts of the dynamics, which leads, for instance, to a Hamiltonian form of gradient dynamics. Moreover, the lifted vector fields can be split into their holonomic and vertical representatives, which provides a geometric method of dynamic reduction. The lifted dynamics can be also given physical meaning, here called the rate-GENERIC. Finally, the lifts can be formulated within contact geometry, where the second law of thermodynamics is explicitly contained within the evolution equations. 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
32
Pages from-to
122902
UT code for WoS article
000898206300003
EID of the result in the Scopus database
2-s2.0-85144340863