Thermodynamic consistency and fluctuations in mesoscopic stochastic simulations of reactive gas mixtures

TL;DR

This paper emphasizes the importance of thermodynamic consistency in mesoscopic fluctuating hydrodynamics simulations of reactive gas mixtures, deriving conditions for reaction rates and validating the approach through numerical experiments.

Contribution

It introduces a thermodynamically consistent reaction (TCR) model ensuring correct fluctuation behavior in reactive gas simulations and derives explicit conditions for rate constants.

Findings

TCR model reproduces correct equilibrium fluctuation statistics.

Temperature variance matches thermodynamic predictions away from walls.

Deviations occur near walls where the system is far from equilibrium.

Abstract

It is essential that mesoscopic simulations of reactive systems reproduce the correct statistical distributions at thermodynamic equilibrium. By considering a compressible fluctuating hydrodynamics (FHD) simulation method of ideal gas mixtures undergoing reversible reactions described by the chemical Langevin equations, we show that thermodynamic consistency in reaction rates and the use of instantaneous temperatures for the evaluation of reaction rates is required for fluctuations for the overall system to be correct. We then formulate the required properties of a thermodynamically-consistent reaction (TCR) model. As noted in the literature, while reactions are often discussed in terms of forward and reverse rates, these rates should not be modeled independently because they must be compatible with thermodynamic equilibrium for the system. Using a simple TCR model where each chemical species has constant heat capacity, we derive the explicit condition that the forward and reverse reaction rate constants must satisfy in order for the system to be thermodynamically consistent. We perform equilibrium and non-equilibrium simulations of ideal gas mixtures undergoing a reversible dimerization reaction to measure the fluctuational behavior of the system numerically. We confirm that FHD simulations with the TCR model give the correct static structure factor of equilibrium fluctuations. For the statistically steady simulation of a gas mixture between two isothermal walls with different temperatures, we show using the TCR model that the temperature variance agrees with the corresponding thermodynamic-equilibrium temperature variance in the interior of the system, whereas noticeable deviations are present in regions near walls, where chemistry is far from equilibrium.