"Chaotic" kinetics, macroscopic fluctuations and longterm stability of the catalytic systems
Abstract
Our recent interest is focused on establishing the necessary and sufficient conditions that guarantee a longterm stable evolution of both natural and artificial systems. Two necessary conditions, called global and local boundedness, are that a system stays stable if and only if the amount and the rate of exchange of energy and/or matter currently involved in any transition do not exceed the thresholds of stability of the system. The relationship between the local and global boundedness and the stability of the system introduces two new general properties of the state space and the motion in it, namely: the state space is always bounded, the successive steps of motion are always finite and involve only nearest neighbors. An immediate consequence of the boundedness is that the invariant measure of the state space is the normal distribution. The necessary condition for the asymptotic stability of the invariant measure is derived. It is found out that the state space exhibits strong chaotic properties regardless to the particularities of the system considered. An example of kinetics that is compatible with both global and local boundedness is considered.
 Publication:

arXiv eprints
 Pub Date:
 April 2004
 arXiv:
 arXiv:condmat/0404312
 Bibcode:
 2004cond.mat..4312K
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Other;
 Mathematical Physics;
 Mathematics  Mathematical Physics;
 Mathematics  Probability;
 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 25 pages, 6 figures