General Expression for the Chemical System Response to External Impact

TL;DR

This paper introduces an improved general map for discrete thermodynamics of chemical systems, enabling better understanding and visualization of system responses to external impacts, including bifurcation and chaotic behaviors.

Contribution

It unifies previous map types into a single, more flexible model that captures a wider range of chemical system responses and aligns more closely with experimental observations.

Findings

Graphical solutions reveal monostable and bistable regions.

Bifurcation diagrams show chaotic oscillations under increased external impact.

Model aligns with experimental electrochemical system graphs.

Abstract

The paper presents amended basic map of states of chemical systems in discrete thermodynamics of chemical equilibria. Uniting two previously found basic map types in one and covering a wider range of situations, it allows us to obtain more detailed pictures and deeper understanding of what is the general chemical system response to the external impact. Amended in this work general expression allows for more flexibility in the response treatment. Graphical solutions to the map, bifurcation diagrams, contain the monostable thermodynamic branch prior to and the bi-stable area after the bifurcation point. On the static diagrams the first consists of two areas - true thermodynamic equilibrium and open equilibrium; the first area is skipped on the dynamic diagrams. In the bi-stable area, the system stresses, caused by further increase of the external impact, discharge themselves through chaotic oscillations, enveloped by two bifurcation sub-branches. Now bifurcation diagrams, corresponding to the amended map, are essentially closer to some experimental graphs, obtained, for instance, in experiments with electrochemical systems.