Discreteness-Induced Criticality in Random Catalytic Reaction Networks

TL;DR

This paper demonstrates that small molecule numbers in random catalytic networks induce universal intermittent dynamics with power-law statistics, revealing a phase transition driven by flow rate changes.

Contribution

It introduces the concept of discreteness-induced criticality in catalytic networks, showing universal power-law behavior in reaction dynamics due to stochastic effects.

Findings

Power-law distributions with exponents 4/3 and 3/2 in reaction event frequency and duration.

A phase transition from stationary to intermittent dynamics as flow rate decreases.

Universal behavior explained by a one-dimensional random walk model.

Abstract

Universal intermittent dynamics in a random catalytic reaction network, induced by smallness in the molecule number is reported. Stochastic simulations for a random catalytic reaction network subject to a flow of chemicals show that the system undergoes a transition from a stationary to an intermittent reaction phase when the flow rate is decreased. In the intermittent reaction phase, two temporal regimes with active and halted reactions alternate. The number frequency of reaction events at each active regime and its duration time are shown to obey a universal power laws with the exponents 4/3 and 3/2, respectively. These power laws are explained by a one-dimensional random walk representation of the number of catalytically active chemicals. Possible relevance of the result to intra-cellular reaction dynamics is also discussed.