[[IJCsatellite/nlin]]
 
  Paper: nlin.SI/0504007
  Date: Mon, 4 Apr 2005 09:30:01 GMT   (12kb)
 
 Title: Canonical Gibbs distribution and thermodynamics of mechanical systems
   with a finite number of degrees of freedom
 
 Authors: V. V. Kozlov
 
 Comments: 15 pages
 
 Subj-class: Exactly Solvable and Integrable Systems
 
 Journal-ref: Regular and Chaotic Dynamics, 1999 Volume 4 Number 2
 
 Traditional derivation of Gibbs canonical distribution and the justification
 of thermodynamics are based on the assumption concerning an isoenergetic
 ergodicity of a system of $n$ weakly interacting identical subsystems and
 passage to the limit $n?to?infty$. In the presented work we develop another
 approach to these problems assuming that $n$ is fixed and $n?ge2$. The ergodic
 hypothesis (which frequently is not valid due to known results of the
 KAM-theory) is substituted by a weaker assumption that the perturbed system
 does not have additional first integrals independent of the energy integral.
 The proof of nonintegrability of perturbed Hamiltonian systems is based on the
 Poincare method. Moreover, we use the natural Gibbs assumption concerning a
 thermodynamic equilibrium of bsystems at vanishing interaction. The general
 results are applied to the system of the weakly connected pendula. The
 averaging with respect to the Gibbs measure allows to pass from usual dynamics
 of mechanical systems to the classical thermodynamic model.
 
 ( http://arXiv.org/abs/nlin/0504007 ,  12kb)
 
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