Stochastic action principle and maximum entropy
Abstract
A stochastic action principle for stochastic dynamics is revisited. We present first numerical diffusion experiments showing that the diffusion path probability depend exponentially on average Lagrangian action. This result is then used to derive an uncertainty measure defined in a way mimicking the heat or entropy in the first law of thermodynamics. It is shown that the path uncertainty (or path entropy) can be measured by the Shannon information and that the maximum entropy principle and the least action principle of classical mechanics can be unified into a concise form. It is argued that this action principle, hence the maximum entropy principle, is simply a consequence of the mechanical equilibrium condition extended to the case of stochastic dynamics.
Cite
@article{arxiv.0704.0880,
title = {Stochastic action principle and maximum entropy},
author = {Q. A. Wang and F. Tsobnang and S. Bangoup and F. Dzangue and A. Jeatsa and A. Le Méhauté},
journal= {arXiv preprint arXiv:0704.0880},
year = {2020}
}
Comments
This work is a further development of the idea proposed in the paper cond-mat/0407515, 15 pages