Information and Helical Mechanism of Entropy Increase

TL;DR

This paper explores the fundamental mechanisms behind entropy increase in dynamical systems, linking information theory, chaos, and physical dissipation to explain irreversibility and the origin of complex phenomena.

Contribution

It introduces a novel perspective on entropy transfer and dissipation mechanisms, connecting local entropy increase with Lyapunov exponents in dynamical systems.

Findings

Entropy transfer from small to macro scales is essential for chaos formation.

Local entropy increase correlates with Lyapunov exponents.

Dissipation mechanisms explain entropy increase in physical systems.

Abstract

The principle of entropy increase is not only the basis of statistical mechanics, but also closely related to the irreversibility of time, the origin of life, chaos and turbulence. In this paper, we first discuss the dynamic system definition of entropy from the perspective of symbol and partition of information, and propose the entropy transfer characteristics based on the set partition. By introducing the hypothesis of limited accuracy of measurement into the continuous dynamical system, two necessary mechanisms for the formation of chaos are obtained: the transfer of entropy from small scale to macro scale (i.e. the increase of local entropy) and the dissipation of macro information. The relationship between the local entropy increase and Lyapunov exponent of dynamical system is established. And then the entropy increase and abnormal dissipation mechanism in physical system are analyzed and discussed.