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Thermodynamics of Hamiltonian systems and the Gibbs distribution. (Russian) Zbl 1023.37002
The author considers generalized coordinates and conjugated canonical momenta of the Hamiltonian system. According to Gibbs, the statistical consideration of Hamiltonian systems relies upon the distribution of the probability density $$\rho = c \exp(-\beta H)$$ where $$c =\text{const} > 0, \beta = kT^{-1}$$, $$T$$ is the absolute temperature and $$k$$ is the Boltzmann constant. The goal here is to propose a rational approach to deduce the canonical distribution for systems of general type.
##### MSC:
 37A60 Dynamical aspects of statistical mechanics 82B05 Classical equilibrium statistical mechanics (general)