Theoretical and Mathematical Physics

, Volume 157, Issue 1, pp 1484–1490 | Cite as

Thermodynamics from the differential geometry standpoint

  • V. P. PavlovEmail author
  • V. M. Sergeev


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 蝃 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.


symplectic structure space of states dynamical principle 


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Copyright information

© MAIK/Nauka 2008

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRASMoscowRussia
  2. 2.Center for Studying Global ProblemsMoscow State Institute of International RelationsMoscowRussia

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