Application of variational methods in chemical thermodynamics: a study of the stability of chemical systems

• Published in: Journal of mathematical chemistry Vol. 53; no. 6; pp. 1380 - 1392
• Main Authors: Reis, Martina Costa, Bassi, Adalberto Bono Maurizio Sacchi
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.06.2015
• Subjects: Chemistry; Chemistry and Materials Science; Math. Applications in Chemistry; Original Paper; Physical Chemistry; Theoretical and Computational Chemistry; Non-equilibrium thermodynamics; Dilute electrolyte solutions; Extremum principles in thermodynamics; Variational methods
• ISSN: 0259-9791; 1572-8897
• DOI: 10.1007/s10910-015-0494-6

The stability of chemical systems is discussed by using elementary concepts of control theory, and Lyapunov stability theory. From these concepts, a mathematically clear definition of irreversible thermodynamic processes and equilibrium states is established. Furthermore, it is shown that the extremum principles of classical thermodynamics can be obtained as natural consequences of the Lyapunov stability theory application in usual physicochemical systems. It is also demonstrated that for the case of chemical systems subject to more general physical conditions, it is possible to find a scalar function dependent of macroscopic parameters that describes the evolution of the system toward the equilibrium state. The aim of this work is to show that by using variational methods one can discuss the stability of many chemical systems.