Russian Journal of Nonlinear Dynamics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Rus. J. Nonlin. Dyn.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Rus. J. Nonlin. Dyn., 2020, Volume 16, Number 4, Pages 557–580 (Mi nd729)  

Nonlinear physics and mechanics

Hamiltonian Thermodynamics

S. A. Rashkovskiyab

a Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, prosp. Vernadskogo 101/1, Moscow, 119526 Russia
b Tomsk State University, ul. Lenina 36, Tomsk, 634050 Russia

Abstract: It is believed that thermodynamic laws are associated with random processes occurring in the system and, therefore, deterministic mechanical systems cannot be described within the framework of the thermodynamic approach. In this paper, we show that thermodynamics (or, more precisely, a thermodynamically-like description) can be constructed even for deterministic Hamiltonian systems, for example, systems with only one degree of freedom. We show that for such systems it is possible to introduce analogs of thermal energy, temperature, entropy, Helmholtz free energy, etc., which are related to each other by the usual thermodynamic relations. For the Hamiltonian systems considered, the first and second laws of thermodynamics are rigorously derived, which have the same form as in ordinary (molecular) thermodynamics. It is shown that for Hamiltonian systems it is possible to introduce the concepts of a thermodynamic state, a thermodynamic process, and thermodynamic cycles, in particular, the Carnot cycle, which are described by the same relations as their usual thermodynamic analogs.

Keywords: Hamiltonian system, adiabatic invariants, thermodynamics, temperature, heat, entropy, thermodynamic processes, the first and second laws of thermodynamics

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation AAAA-A20-120011690135-5
This work was carried out in accordance with the State Assignment No. AAAA-A20-120011690135-5. Funding was provided in part by the Tomsk State University Competitiveness Improvement Program.


DOI: https://doi.org/10.20537/nd200403

Full text: PDF file (390 kB)
References: PDF file   HTML file

Bibliographic databases:

MSC: 70H05, 70H11, 70H12, 70K70
Received: 07.10.2020
Accepted:27.11.2020

Citation: S. A. Rashkovskiy, “Hamiltonian Thermodynamics”, Rus. J. Nonlin. Dyn., 16:4 (2020), 557–580

Citation in format AMSBIB
\Bibitem{Ras20}
\by S. A. Rashkovskiy
\paper Hamiltonian Thermodynamics
\jour Rus. J. Nonlin. Dyn.
\yr 2020
\vol 16
\issue 4
\pages 557--580
\mathnet{http://mi.mathnet.ru/nd729}
\crossref{https://doi.org/10.20537/nd200403}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=4198780}


Linking options:
  • http://mi.mathnet.ru/eng/nd729
  • http://mi.mathnet.ru/eng/nd/v16/i4/p557

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Russian Journal of Nonlinear Dynamics
    Number of views:
    This page:37
    Full text:28
    References:2

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021