Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2004-10-08
Physics
Condensed Matter
Statistical Mechanics
version2 with typing corrections
Scientific paper
We present certain mathematical aspects of an information method which was formulated in an attempt to investigate diffusion phenomena. We imagine a regular dynamical hamiltonian systems under the random perturbation of thermal (molecular) noise and chaotic motion. The random effect is taken into account via the uncertainty of irregular dynamic process produced in this way. This uncertainty due to different paths between two phase points is measured by a path information which is maximized in connection with the action defined originally for the unperturbed regular hamiltonian systems. The obtained transition probability depends exponentially on this action. The usefulness of this information method has been demonstrated by the derivation of diffusion laws without the usual assumptions. In this work, some essential mathematical aspects of this irregular dynamics is reviewed. It is emphasized that the classical action principle for single least action path is no more valid and the formalism of classical mechanics for regular hamiltonian systems is no more exact for irregular hamiltonian dynamics. There is violation of the fundamental laws of mechanics by randomly perturbed hamiltonian systems. However, the action principle is always present for the ensemble of paths through the average action. This average action principle leads to a formalism of stochastic mechanics in which, in spite of the violation of fundamental laws, the mathematical form of classical mechanics can be recovered by a consideration of the statistical averaging of the dynamics.
Li Wangrong
Wang Qiuping A.
No associations
LandOfFree
A mathematical method for irregular hamiltonian systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A mathematical method for irregular hamiltonian systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A mathematical method for irregular hamiltonian systems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-315918