Temporary mirror symmetry breaking and chiral excursions in open and closed systems

TL;DR

This paper investigates how initial chiral deviations are temporarily amplified in the reversible Frank model and how the system's openness influences whether it reaches a permanent chiral state or remains racemic.

Contribution

It combines phase space, stability analysis, and simulations to understand chiral excursions and their dependence on system openness in the Frank model.

Findings

Open systems can reach permanent chirality.

Closed systems tend to remain racemic.

Chiral excursions are transient phenomena influenced by system openness.

Abstract

The reversible Frank model is capable of amplifying the initial small statistical deviations from the idealized racemic composition. This temporary amplification can be interpreted as a chiral excursion in a dynamic phase space. It is well known that if the system is open to matter and energy exchange, a permanently chiral state can be reached asymptotically, while the final state is necessarily racemic if the system is closed. In this work, we combine phase space analysis, stability analysis and numerical simulations to study the initial chiral excursions and determine how they depend on whether the system is open, semi-open or closed.