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This article is cited in 6 scientific papers (total in 6 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
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
DOI:
https://doi.org/10.4213/tmf6269
 Full text:
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English version:
Theoretical and Mathematical Physics, 2008, 157:1, 1484–1490
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Document Type:
Article
Received: 19.11.2007
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
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Linking options:
http://mi.mathnet.ru/eng/tmf6269https://doi.org/10.4213/tmf6269 http://mi.mathnet.ru/eng/tmf/v157/i1/p141
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