Journal ArticleDOI
Long range correlations and the onset of chemical instabilities
Reads0
Chats0
TLDR
In this paper, the authors analyzed the coherence length beyond which fluctuations can amplify and induce instabilities at a macroscopic scale and established the existence of diverging form factors and long range correlations.Abstract:
Recent analyses of fluctuations in non-equilibrium systems by Prigogine, Malek-Mansour and Nicolis have indicated the existence of a minimal coherence length beyond which fluctuations can amplify and induce instabilities at a macroscopic scale. Conversely, this observation suggests the emergence of long range spatial correlations in systems undergoing non-equilibrium unstable transitions. In the present paper, this problem is analyzed for reaction-diffusion systems and illustrated on a specific model. The existence of diverging form factors and of long range correlations is established. The connection between the multi-variate master equation and the local equation developed recently by Prigogine, Malek-Mansour and Nicolis is discussed.read more
Citations
More filters
Journal ArticleDOI
Time, structure, and fluctuations.
TL;DR: It is shown that nonequilibrium may become a source of order and that irreversible processes may lead to a new type of dynamic states of matter called "dissipative structures" and the thermodynamic theory of such structures is outlined.
Journal ArticleDOI
The Poisson Representation. I. A New Technique for Chemical Master Equations
TL;DR: In this article, a new technique for handling chemical master equations, based on an expansion of the probability distribution in Poisson distributions, is introduced, which enables chemical master equation to be transformed into Fokker-Planck and stochastic differential equations and yields very simple descriptions of chemical equilibrium states.
Journal ArticleDOI
Asymptotic properties of markovian master equations
TL;DR: In this paper, an asymptotic method of analysis of fluctuations in systems far from equilibrium is developed, using singular perturbative expansion of the equation for the generating function, using as smallness parameter the inverse of the size of the system.
Journal ArticleDOI
Reaction-diffusion master equation : a comparison with microscopic simulations
Florence Baras,M. Malek Mansour +1 more
Journal ArticleDOI
Nonlinear Kinetics and New Approaches to Complex Reaction Mechanisms
John Ross,Marcel Ovidiu Vlad +1 more
TL;DR: This paper reviews recent developments in the field of nonlinear chemical kinetics and discusses new approaches to complex reaction mechanisms, stoichiometric network analysis, classification of chemical oscillators and formulation of their mechanisms by deduction from experiments, and correlation metric construction of reaction pathways from measurements.
References
More filters
Journal ArticleDOI
Statistical-Mechanical Theory of Irreversible Processes : I. General Theory and Simple Applications to Magnetic and Conduction Problems
TL;DR: In this paper, a general type of fluctuation-dissipation theorem is discussed to show that the physical quantities such as complex susceptibility of magnetic or electric polarization and complex conductivity for electric conduction are rigorously expressed in terms of timefluctuation of dynamical variables associated with such irreversible processes.
Journal ArticleDOI
Symmetry Breaking Instabilities in Dissipative Systems. II
Ilya Prigogine,René Lefever +1 more
TL;DR: The thermodynamic theory of symmetry breaking instabilities in dissipative systems is presented in this article, where several kinetic schemes which lead to an unstable behavior are indicated, and the role of diffusion is studied in more detailed way.
Journal ArticleDOI
Fluctuations in Nonequilibrium Systems
Grégoire Nicolis,I. Prigogine +1 more
TL;DR: The theory of fluctuations is extended to nonlinear systems far from equilibrium, in which the departure from the steady state is governed by large fluctuations of macroscopic size, while small thermal fluctuations are still described by a generalization of Einstein's equilibrium theory.
Journal ArticleDOI
Fluctuations around nonequilibrium states in open nonlinear systems
TL;DR: In this paper, the theory of nonequilibrium fluctuations in open systems is extended to nonlinear situations, and it is shown that the usual birth-and-death type of stochastic formulation of chemical kinetics is in general inadequate and has to be replaced by a more detailed phase-space description.