Qualms Regarding the Range of Validity of the Glansdorff-Prigogine Criterion for Stability of Non-Equilibrium States | Zendy

Joel Keizer | Zendy; Ronald F. Fox | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Qualms Regarding the Range of Validity of the Glansdorff-Prigogine Criterion for Stability of Non-Equilibrium States

Author(s) -

Joel Keizer,

Ronald F. Fox

Publication year - 1974

Publication title -

proceedings of the national academy of sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 5.011

H-Index - 771

eISSN - 1091-6490

pISSN - 0027-8424

DOI - 10.1073/pnas.71.1.192

Subject(s) - stability (learning theory) , autocatalysis , statistical physics , stability criterion , thermodynamics , mathematical economics , autocatalytic reaction , range (aeronautics) , economics , mathematics , physics , statistics , computer science , classical mechanics , kinetics , materials science , discrete time and continuous time , machine learning , composite material

Doubt is raised concerning the range of validity of a stability criterion for non-equilibrium states which has been proposed by Glansdorff and Prigogine. In the case of a particular autocatalytic reaction, the stability analysis presented by Glansdorff and Prigogine, and by Eigen and by Katchalsky in their reviews of this problem, does not agree with our analysis, which is based upon exact solution of the relevant rate equations. We also find disagreement between the analysis based upon the Glansdorff-Prigogine criterion and our analysis of a second example which involves non-equilibrium steady states. The situation is quite delicate because seemingly innocent approximations (e.g., the use of specialized conditions in the autocatalytic reactionX +Y ⇄ 2X discussed in the sequel) may lead to the impression that the scope of validity of the criterion is wider than it actually is. By considering the stability of the equilibrium state, we conclude that the second differential of the entropy, which is at the heart of the Glansdorff-Prigogine criterion, is likely to be relevant for stability questions close to equilibrium only.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research