A. S. Trushechkin, “Irreversibility and the role of an instrument in the functional formulation of classical mechanics”, TMF, 164:3 (2010), 435–440; Theoret. and Math. Phys., 164:3 (2010), 1198

Loading [MathJax]/jax/output/SVG/config.js

Teoreticheskaya i Matematicheskaya Fizika

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor
	Guidelines for authors
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

TMF:
Year:
Volume:
Issue:
Page:
	Find

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

Teoreticheskaya i Matematicheskaya Fizika, 2010, Volume 164, Number 3, Pages 435–440
DOI: https://doi.org/10.4213/tmf6554 (Mi tmf6554)

This article is cited in 10 scientific papers (total in 10 papers)

Irreversibility and the role of an instrument in the functional formulation of classical mechanics

A. S. Trushechkin

Steklov Mathematical Institute, RAS, Moscow, Russia

Full-text PDF (339 kB) Citations (10)

References:

PDF

HTML

DOI: https://doi.org/10.4213/tmf6554

Abstract: We analyze the role of an instrument in the recently proposed functional formulation of classical mechanics, whose basic equation is the Liouville equation. Its solution has the delocalization (spreading) property, which is interpreted as irreversibility on the microlevel. We show that the reversible and recurrent dynamics for a particle can be observed by tracking the particle dynamics using instruments, but repeated measurements inevitably lead to a heat release and an increase in the entropy of the instrument. The irreversible behavior is thus transported from the system under study to the instrument, which is also a physical system.

Keywords: classical mechanics, irreversibility problem, Liouville equation, measurement theory.

English version:
Theoretical and Mathematical Physics, 2010, Volume 164, Issue 3, Pages 1198–1201
DOI: https://doi.org/10.1007/s11232-010-0100-9

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: A. S. Trushechkin, “Irreversibility and the role of an instrument in the functional formulation of classical mechanics”, TMF, 164:3 (2010), 435–440; Theoret. and Math. Phys., 164:3 (2010), 1198–1201

Citation in format AMSBIB

\Bibitem{Tru10}

\by A.~S.~Trushechkin

\paper Irreversibility and the~role of an~instrument in the~functional formulation of classical mechanics

\jour TMF

\yr 2010

\vol 164

\issue 3

\pages 435--440

\mathnet{http://mi.mathnet.ru/tmf6554}

\crossref{https://doi.org/10.4213/tmf6554}

\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2010TMP...164.1198T}

\transl

\jour Theoret. and Math. Phys.

\yr 2010

\vol 164

\issue 3

\pages 1198--1201

\crossref{https://doi.org/10.1007/s11232-010-0100-9}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000282695500013}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77958027819}

Linking options:

https://www.mathnet.ru/eng/tmf6554

https://doi.org/10.4213/tmf6554

https://www.mathnet.ru/eng/tmf/v164/i3/p435

This publication is cited in the following 10 articles:

Casey O Barkan, “On the convergence of phase space distributions to microcanonical equilibrium: dynamical isometry and generalized coarse-graining”, J. Phys. A: Math. Theor., 57:47 (2024), 475001
Trushechkin A., “Microscopic and Soliton-Like Solutions of the Boltzmann Enskog and Generalized Enskog Equations For Elastic and Inelastic Hard Spheres”, Kinet. Relat. Mod., 7:4 (2014), 755–778
A. I. Mikhailov, “Infinitnoe dvizhenie v klassicheskoi funktsionalnoi mekhanike”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(30) (2013), 222–232
I. V. Volovich, A. S. Trushechkin, “Asymptotic properties of quantum dynamics in bounded domains at various time scales”, Izv. Math., 76:1 (2012), 39–78
A. S. Trushechkin, “Uravnenie Boltsmana i $H$-teorema v funktsionalnoi formulirovke klassicheskoi mekhaniki”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(22) (2011), 158–164
A. I. Mikhailov, “The functional mechanics: Evolution of the moments of distribution function and the Poincaré recurrence theorem”, P-Adic Numbers, Ultrametric Analysis, and Applications, 3:3 (2011), 205–211
Anton S. Trushechkin, “Derivation of the Boltzmann equation and entropy production in functional mechanics”, P-Adic Num Ultrametr Anal Appl, 3:3 (2011), 225
E. V. Piskovskii, “O klassicheskom i funktsionalnom podkhodakh k mekhanike”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(22) (2011), 134–139
E. V. Piskovskiy, “On classical and functional approachs to mechanics”, –
I. V. Volovich, “Bogoliubov equations and functional mechanics”, Theoret. and Math. Phys., 164:3 (2010), 1128–1135

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	641
Full-text PDF :	302
References:	113
First page:	20

Registration to the website

Logotypes