The failure of the master equation for the reactive systems

TL;DR

This paper critiques the fundamental assumptions behind the master equation in reactive systems, highlighting issues with state variable definitions and divergence problems that undermine its applicability.

Contribution

It identifies key reasons why the master equation fails in reactive systems, proposing novel perspectives on low-energy limits and system evolution.

Findings

State variables must be insensitive to spatio-temporal configurations.

Divergence of scattering length causes divergence of elementary process rates.

Master equation remains inappropriate despite new viewpoints.

Abstract

Two crucial for the breakdown of the master equation arguments are put forward. The first one is related to the violence of a fundamental requirement to the notion of state (thermodynamical) variable, namely: a state variable is defined provided it is insensitive to the particularities of the spatio-temporal configurations upon which the averaging over the dynamical variables proceeds. The second one is related to a ubiquitous divergence of the scattering length in the low-energy limit. In turn, it makes the rates of all the elementary processes divergent as well. Though radically novel viewpoints to the low-energy limit and to the evolution ensure the boundedness of the rates and hold the notion of a state variable available, the master equation remains inappropriate.