Stationary solutions of the master equation for single and multi-intermediate autocatalytic chemical systems

Journal Article · Wed Jan 01 04:00:00 EST 1992 · Journal of Chemical Physics; (United States)

DOI:https://doi.org/10.1063/1.462446· OSTI ID:5524123

Zheng, Q; Ross, J ^[1]; Hunt, K L.C.; Hunt, P M ^[2]

---

1. Department of Chemistry, Stanford University, Stanford, California 94305 (United States)
2. Department of Chemistry, Michigan State University, East Lansing, Michigan 48824 (United States)

In this work, we test a hypothesized form for the stationary solution {ital P}{sub {ital s}}({ital X},{ital Y}) of the stochastic master equation for a reacting chemical system with two reactive intermediates {ital X} and {ital Y}, and multiple steady states. Thermodynamic analyses and the exact results for nonautocatalytic or equilibrating systems suggest an approximation of the form {ital P}{sup {ital a}}{sub {ital s}}({ital X},{ital Y})=N exp({minus}{phi}/{ital kT}), where the function {phi} is a line integral of a differential excess'' work F{phi}, which depends on species-specific affinities. The differential F{phi} is inexact. In a preceding paper, we have given an analytic argument for the use of the deterministic kinetic trajectory, connecting ({ital X},{ital Y}) to the steady state ({ital X}{sup {ital s}},{ital Y}{sup {ital s}}) as the path of integration for F{phi}. Here, we show that use of the deterministic trajectories leads to a potential {phi}{sub det} which is continuous across the separatrix between the domains of attraction of the two stable steady states in the model studied.

• OSTI ID: 5524123
• Journal Information: Journal of Chemical Physics; (United States), Journal Name: Journal of Chemical Physics; (United States) Vol. 96:1; ISSN JCPSA; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
400201* -- Chemical & Physicochemical Properties
ANALYTICAL SOLUTION
CATALYSIS
CHEMICAL REACTIONS
EQUILIBRIUM
FEYNMAN PATH INTEGRAL
INTEGRALS
STABILITY
STEADY-STATE CONDITIONS
THERMODYNAMICS
TIME DEPENDENCE
TRAJECTORIES