Statistical ensemble approach and fluctuation-dissipation relations for multivariable chemical systems far from equilibrium
A statistical ensemble approach and an ensemble master equation are introduced for the study of concentration fluctuations in multivariable chemical systems far from equilibrium. The theory describes the stochastic properties of the numbers of replicas of the system characterized by different compositions. The authors give a general analytic solution of the ensemble master equation and investigate the relationships between the ensemble master equation and the one-system master equation. A condition of mesoscopic time reversal (mesoscopic reversibility) is introduced for a reference system; mesoscopic reversibility is less restrictive than microscopic reversibility. For systems with mesoscopic time reversal the general theory turns into a simple form and, in the thermodynamic limit, an exact expression for the stochastic potential attached to the one-system master equation is derived. The stochastic properties of the numbers of the reaction events both for system with or without mesoscopic time reversal are studied. The condition of mesoscopic time reversal can be described by an extremum condition: if the contributions of different reactions to the total number of reaction events are constant, then the dispersions of the net numbers of the reaction events have minimum values for mesoscopic reversibility. A set of fluctuation-dissipation relations is derived for multivariable chemical systems, based on the use of the reaction extents as state variables of the system. Systems that do not obey the condition of mesoscopic time reversal are considered and the departure of a chemical process from mesoscopic reversibility in terms of a set of functions is measured, which are proportional to the average values of the net numbers of the reaction events. In terms of these functions a set of fluctuation-dissipation relations that establish a general relationship among the rates and the reaction affinities of the different reactions occurring in the system are derived. A component of the dissipation function of the process is computed by using these fluctuation-dissipation relations.
- Research Organization:
- Stanford Univ., CA (US)
- Sponsoring Organization:
- National Science Foundation (NSF); USDOE
- OSTI ID:
- 20034407
- Journal Information:
- Journal of Physical Chemistry A: Molecules, Spectroscopy, Kinetics, Environment, amp General Theory, Vol. 104, Issue 14; Other Information: PBD: 13 Apr 2000; ISSN 1089-5639
- Country of Publication:
- United States
- Language:
- English
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