Generic two-phase coexistence in nonequilibrium systems

TL;DR

This paper discusses the phenomenon of generic two-phase coexistence in nonequilibrium systems, which can occur over finite regions of parameter space, challenging traditional phase rules and with implications in physics, biology, and computer science.

Contribution

It introduces the concept of generic multistability in nonequilibrium systems, exemplified by Toom's model, and explores its significance across various scientific fields.

Findings

Two-phase coexistence can occur over finite parameter regions in nonequilibrium systems.

Generic multistability has practical applications in biology and computer science.

The behavior challenges classical phase rules like Gibbs' phase rule.

Abstract

Gibbs' phase rule states that two-phase coexistence of a single-component system, characterized by an n-dimensional parameter-space, may occur in an n-1-dimensional region. For example, the two equilibrium phases of the Ising model coexist on a line in the temperature-magnetic-field phase diagram. Nonequilibrium systems may violate this rule and several models, where phase coexistence occurs over a finite (n-dimensional) region of the parameter space, have been reported. The first example of this behaviour was found in Toom's model [Toom,Geoff,GG], that exhibits generic bistability, i.e. two-phase coexistence over a finite region of its two-dimensional parameter space (see Section 1). In addition to its interest as a genuine nonequilibrium property, generic multistability, defined as a generalization of bistability, is both of practical and theoretical relevance. In particular, it has been used recently to argue that some complex structures appearing in nature could be truly stable rather than metastable (with important applications in theoretical biology), and as the theoretical basis for an error-correction method in computer science (see [GG,Gacs] for an illuminating and pedagogical discussion of these ideas).