Irreversible Circulation and Orbital Revolution: Hard Mode Instability in Far-from-Equilibrium Situation

Abstract

The need and the use of the concept of cyclic balance and irreversible circulation are demonstrated by a chemically reacting system with two independent degrees of freedom. Under the presence of auto-catalytic channel, the reaction network may lead to instabilities at a certain threshold for the controllable major reactant. Attention is concentrated on the hard mode instability in particular, which leads to an orbital revolution of the distribution function. By looking at the evolution of fluctuation as well as the drift, one finds that the irreversible circulation becomes singular at the marginal situation. The resulting limit cycle is just a macroscopic manifestation of the dynamically directed property which is latent in the fluctuation below threshold. The state beyond the threshold is analyzed with Prigogine-Lefever-Nicolis model. Emphasis is placed on the fact that temporal oscillation is a new type of order which appears only far from equilibrium.