Geodesic
Thermodynamics from the~differential geometry standpoint
Teoretičeskaâ i matematičeskaâ fizika, Tome 157 (2008) no. 1, pp. 141-148

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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. 
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     author = {V. P. Pavlov and V. M. Sergeev},
     title = {Thermodynamics from the~differential geometry standpoint},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {141--148},
     publisher = {mathdoc},
     volume = {157},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2008_157_1_a9/}
}
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V. P. Pavlov; V. M. Sergeev. Thermodynamics from the~differential geometry standpoint. Teoretičeskaâ i matematičeskaâ fizika, Tome 157 (2008) no. 1, pp. 141-148. http://geodesic.mathdoc.fr/item/TMF_2008_157_1_a9/