Least action principle and stochastic motion : a generic derivation of path probability

4th International Workshop on Statistical Physics and Mathematics for Complex Systems

物理学;数学

Kaabouchi, Aziz El^1 ; Wang, Qiuping A.^1,2

ISMANS, LUNAM Université, F.A. Bartholdi, 44, Avenue, Le Mans

72000, France^1

IMMM, UMR CNRS 6283, Université du Mainé, Le Mans

72085, France^2

关键词: Analytical calculation;    Dissipated energy;    Exponential dependence;    Langevin equation;    Least action principle;    Mechanical systems;    Path probability;    Stochastic motion;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/604/1/012011/pdf
DOI  :  10.1088/1742-6596/604/1/012011

来源: IOP

【 摘 要 】

This work is an analytical calculation of the path probability for random dynamics of mechanical system described by Langevin equation with Gaussian noise. The result shows an exponential dependence of the probability on the action. In the case of non dissipative limit, the action is the usual one in mechanics in accordance with the previous result of numerical simulation of random motion. In the case of dissipative motion, the action in the exponent of the exponential probability is just the one proposed in a previous work (Q.A. Wang, R. Wang, arXiv:1201.6309), an action defined for the total system including the moving system and its environment receiving the dissipated energy. In both cases, the result implies that the most probable paths are the paths of least action which, in the limit of vanishing randomness, become the regular paths minimizing the action.