Thermodynamic and stochastic theory for nonequilibrium systems with multiple reactive intermediates: The concept and role of excess work

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

DOI:https://doi.org/10.1063/1.462445· OSTI ID:5573906

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

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

We continue our development of a global thermodynamic and stochastic theory of open chemical systems far from equilibrium with an analysis of a broad class of isothermal, multicomponent reaction mechanisms with multiple steady states, studied under the assumption of local equilibrium. We generalize species-specific affinities of reaction intermediates, obtained in prior work for nonautocatalytic reaction mechanisms, to autocatalytic kinetics and define with these affinities an excess free energy differential F{phi}. The quantity F{phi} is the difference between the work required to reverse a spontaneous concentration change and the work available when the same concentration change is imposed on a system in a reference steady state. The integral of F{phi} is in general not a state function; in contrast, the function {phi}{sub det} obtained by integrating F{phi} along deterministic kinetic trajectories is a state function, as well as an identifiable term in the time-integrated dissipation. Unlike the total integrated dissipation, {phi}{sub det} remains finite during the infinite duration of the system's relaxation to a steady state and hence {phi}{sub det} can be used to characterize that process. The variational relation {delta}{phi}{ge}0 is shown to be a necessary and sufficient thermodynamic criterion for a stable steady state in terms of the excess work of displacement of the intermediates and {phi}{sub det} is a Liapunov function in the domain of attraction of such steady states. Based on these results and earlier work with nonautocatalytic and equilibrating systems, we hypothesize that the stationary distribution of the master equation may be obtained in the form {ital P}{sub {ital s}}=N exp({minus}{phi}{sub det}/{ital kT}) and provide an analytical argument for this form for macroscopic systems.

• OSTI ID: 5573906
• 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
AFFINITY
ANALYTICAL SOLUTION
CHEMICAL REACTIONS
ENERGY LEVELS
ENERGY LOSSES
EQUILIBRIUM
EXCITED STATES
FLUCTUATIONS
INTEGRALS
ISOTHERMAL PROCESSES
LOSSES
LYAPUNOV METHOD
RELAXATION
STABILITY
STEADY-STATE CONDITIONS
STOCHASTIC PROCESSES
THERMODYNAMICS
TRAJECTORIES
VARIATIONS
VIBRATIONAL STATES