"Chaotic" kinetics, macroscopic fluctuations and long-term stability of the catalytic systems

TL;DR

This paper investigates the conditions for long-term stability in natural and artificial systems, revealing that boundedness leads to chaotic behavior and a normal distribution of states, with implications for understanding system stability.

Contribution

It introduces the concepts of global and local boundedness as necessary conditions for system stability and explores their implications for the state space and system dynamics.

Findings

State space is always bounded and involves only nearest neighbor steps.

Invariant measure of the state space is normally distributed.

Systems exhibit strong chaotic properties regardless of specifics.

Abstract

Our recent interest is focused on establishing the necessary and sufficient conditions that guarantee a long-term stable evolution of both natural and artificial systems. Two necessary conditions, called global and local boundedness, are that a system stays stable if and only if the amount and the rate of exchange of energy and/or matter currently involved in any transition do not exceed the thresholds of stability of the system. The relationship between the local and global boundedness and the stability of the system introduces two new general properties of the state space and the motion in it, namely: the state space is always bounded, the successive steps of motion are always finite and involve only nearest neighbors. An immediate consequence of the boundedness is that the invariant measure of the state space is the normal distribution. The necessary condition for the asymptotic stability of the invariant measure is derived. It is found out that the state space exhibits strong chaotic properties regardless to the particularities of the system considered. An example of kinetics that is compatible with both global and local boundedness is considered.