Impact of currents on non-equilibrium coexistence in chemically driven mixtures

TL;DR

This paper explores how non-equilibrium currents influence the coexistence of different molecular phases in chemically driven mixtures, revealing generalized criteria for phase equilibrium in biological and physical systems.

Contribution

It introduces a thermodynamically consistent framework for understanding phase coexistence in non-equilibrium mixtures with switching molecules, extending classical Gibbs criteria.

Findings

Derived steady-state coexistence criteria for non-equilibrium mixtures.

Generalized Gibbs' conditions incorporating currents and chemical potential differences.

Demonstrated the balancing of chemical potential differences and currents at interfaces.

Abstract

Virtually every biological function emerges through the organization of molecules in time and space. Consequently, a major challenge in statistical physics is to uncover the universal principles governing macromolecular self-organization within the crowded, non-equilibrium environment of the cell. Here, we investigate a class of models where molecules maintain a conserved total concentration but can switch "identities", thereby modulating their intermolecular interactions. By enforcing thermodynamic consistency via the local detailed balance condition, we derive the steady-state criteria determining coexisting concentrations in a binary mixture. For non-constant transition rates and using a sharp-interface approximation, we obtain jump conditions that generalize Gibbs' coexistence criteria of equal pressure and chemical potential. We demonstrate that these jumps balance the chemical potential differences of individual species against their currents, which are confined to the interfacial region.