Maximum path information and the principle of least action for chaotic system

TL;DR

This paper introduces a probabilistic framework linking maximum path information to the principle of least action in chaotic systems, showing that the most probable paths are those of least action, thus connecting information theory with classical mechanics.

Contribution

It establishes a novel connection between maximum path information and the principle of least action in chaotic systems, deriving transition probabilities from an information-theoretic perspective.

Findings

Most probable paths are paths of least action.

Maximum path information leads to known transition probabilities.

Principle of least action is equivalent to maximizing path information.

Abstract

A path information is defined in connection with the different possible paths of chaotic system moving in its phase space between two cells. On the basis of the assumption that the paths are differentiated by their actions, we show that the maximum path information leads to a path probability distribution as a function of action from which the well known transition probability of Brownian motion can be easily derived. An interesting result is that the most probable paths are just the paths of least action. This suggests that the principle of least action, in a probabilistic situation, is equivalent to the principle of maximization of information or uncertainty associated with the probability distribution.