A Rayleigh criterion for mechanical instability: inducing activity by chemo-mechanical coupling

TL;DR

This paper develops a theoretical framework to identify conditions under which chemical driving induces mechanical activity and rotation, using Rayleigh-like criteria based on phase relations in driven systems.

Contribution

It introduces a novel Rayleigh criterion for mechanical instability in chemo-mechanical systems, linking chemical driving to active motion via phase relations.

Findings

Derived Rayleigh-like criteria for activity onset

Established phase relation conditions for sustained rotation

Linked chemical driving to mechanical activity through theoretical analysis

Abstract

Instabilities in thermodynamic systems are often undesirable, as they can lead to loss of control or even catastrophic behavior. Yet, the same mechanisms can also generate rich nonequilibrium behavior and may play a constructive role in living systems. We introduce a theoretical framework, inspired by Rayleigh's analysis of thermoacoustic instabilities, to study the emergence of mechanical activity. In particular, we derive Rayleigh-like criteria governing the onset of activity and the generation of rotational motion in a slow Newtonian probe coupled to driven chemical processes, described by Markov jump processes. These criteria are expressed in terms of the phase relation between entropic and frenetic contributions, providing a transparent condition for when chemical driving results in sustained rotational or active mechanical motion.