Geodesic
Irreversibility and the role of an instrument in the functional formulation of classical mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 3, pp. 435-440 Cet article a éte moissonné depuis la source Math-Net.Ru

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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, measurement theory.
Mots-clés : Liouville equation 
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A. S. Trushechkin. Irreversibility and the role of an instrument in the functional formulation of classical mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 3, pp. 435-440. http://geodesic.mathdoc.fr/item/TMF_2010_164_3_a12/

[1] I. V. Volovich, Vestn. SamGU. Estestvennonauchnaya ser., 8/1:67 (2008), 35–55; I. V. Volovich, Time irreversibility problem and functional formulation of classical mechanics, 2009, arXiv: 0907.2445

[2] V. V. Kozlov, Teplovoe ravnovesie po Gibbsu i Puankare, Sovremennaya matematika, RKhD, M., Izhevsk, 2002 | MR | Zbl

[3] V. V. Kozlov, Ansambli Gibbsa i neravnovesnaya statisticheskaya mekhanika, RKhD, M., Izhevsk, 2008

[4] V. V. Kozlov, D. V. Treschev, TMF, 151:1 (2007), 120–137 | DOI | MR | Zbl

[5] A. S. Trushechkin, I. V. Volovich, P-Adic Numbers Ultrametric Anal. Appl., 1:4 (2009), 361–367, arXiv: 0910.1502 | DOI | MR | Zbl

[6] L. Szilard, Z. f. Physik, 53:11–12 (1929), 840–856 | DOI | Zbl

[7] C. H. Bennett, Internat. J. Theoret. Phys., 21:12 (1982), 905–940 | DOI

[8] R. Landauer, “Neobratimost i vydelenie tepla v protsesse vychislenii”, Kvantovyi kompyuter i kvantovye vychisleniya, v. 1, 2, ed. V. A. Sadovnichii, Udmurtskii universitet, Izhevsk, 1999, 9–32 | MR | Zbl

[9] B. D. Agapev, V. N. Belov, F. P. Kesmanly, V. V. Kozlovskii, S. I. Markov, Eksperimentalnaya obrabotka rezultatov izmerenii, SPbGTU, SPb., 2001