Phase coexistence in a weakly stochastic reaction-diffusion system.

Area of Science:

• Chemical kinetics
• Statistical mechanics
• Non-equilibrium systems

Background:

• Reaction-diffusion systems are fundamental to understanding pattern formation and complex behaviors in chemistry and biology.
• Phase coexistence, where distinct chemical states coexist, is a key phenomenon in bistable systems.
• Continuum approximations are often used but may obscure discrete effects in spatially extended systems.

Purpose of the Study:

• To investigate phase coexistence in a weakly stochastic reaction-diffusion system without relying on a continuum description.
• To derive a condition for phase coexistence in a system of (2N+1) diffusion-coupled vessels as N approaches infinity.
• To analyze the dependence of phase coexistence on the rate of particle hopping between neighboring vessels.

Main Methods:

• Development of a discrete model for a reaction-diffusion system with bistable kinetics.
• Derivation of the phase coexistence condition in the thermodynamic limit (N→∞).
• Analysis of the system's behavior in high- and low-hopping rate regimes.

Main Results:

• A condition for phase coexistence was derived for the discrete reaction-diffusion system.
• The phase coexistence condition was found to be dependent on the hopping rate between vessels.
• Distinct potentials governing phase coexistence were identified for high- and low-hopping rate limits, derived from the single-vessel reaction kinetics.

Conclusions:

• Phase coexistence in weakly stochastic reaction-diffusion systems can be understood without continuum approximations.
• The hopping rate between discrete spatial locations plays a critical role in determining phase coexistence.
• The derived potentials offer insights into the microscopic mechanisms underlying macroscopic phase separation.