Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2011-01-03
Physics
Condensed Matter
Statistical Mechanics
8 pages? Proceedings of the First Franco-Mongolian Workshop on Material Sciences, August 22-25, 2010, Ulaabaatar, Mongolia, Ts
Scientific paper
Recent result of the numerical simulation of stochastic motion of conservative mechanical or weakly damped Brownian motion subject to conservative forces reveals that, in the case of Gaussian random forces, the path probability depends exponentially on Lagrangian action. This distribution implies a fundamental principle generalizing the least action principle of the Hamiltonian/Lagrangian mechanics and yields an extended formalism of mechanics for random dynamics. Within this theory, Liouville theorem of conservation of phase distribution breaks down. This opens a way to the Boltzmann H theorem. We argue that the randomness is a crucial distinction between two kingdoms of Hamiltonian/Lagrangian mechanics: the stochastic dynamics and the regular one which is a special case of the first one for vanishing randomness. This distinction was missing in the criticisms of this theorem from Loschmidt, Poincar\'e and Zermelo.
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