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Teoreticheskaya i Matematicheskaya Fizika, 2008, Volume 157, Number 1, Pages 141–148
DOI: https://doi.org/10.4213/tmf6269 (Mi tmf6269) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Thermodynamics from the differential geometry standpoint

V. P. Pavlova, V. M. Sergeevb

a Steklov Mathematical Institute, Russian Academy of Sciences
b Moscow State Institute of International Relations (University) of the Ministry for Foreign Affairs of Russia
Full-text PDF (328 kB) Citations (7)
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DOI: https://doi.org/10.4213/tmf6269
Abstract: We study the differential-geometric structure of the space of thermodynamic states in equilibrium thermodynamics. We demonstrate that this space is a foliation of codimension two and find variables in which the foliation fibers are flat. We show that we can introduce a symplectic structure on this space: the external derivative of the $1$-form of the heat source, which has the form of the skew-symmetric product $dT\wedge dS$ in the found variables. The entropy $S$ then plays the role of the Lagrange function (or Hamiltonian) in mechanics, completely determining the thermodynamic system.
Keywords: symplectic structure, space of states, dynamical principle.
Received: 19.11.2007
English version:
Theoretical and Mathematical Physics, 2008, Volume 157, Issue 1, Pages 1484–1490
DOI: https://doi.org/10.1007/s11232-008-0122-8
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. P. Pavlov, V. M. Sergeev, “Thermodynamics from the differential geometry standpoint”, TMF, 157:1 (2008), 141–148; Theoret. and Math. Phys., 157:1 (2008), 1484–1490
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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