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Entropy
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Kinetic Models of Chemical Reactions
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Kinetic Models of Chemical Reactions

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Thermodynamics".

Deadline for manuscript submissions: 31 October 2025 | Viewed by 2180

Special Issue Editors

Prof. Dr. Gregory Yablonsky

E-Mail Website
Guest Editor
McKelvey School of Engineering, Department of Energy, Environmental and Chemical Engineering, Washington University in St. Louis, 1 Brookings Dr., St. Louis, MO 63130, USA
Interests: reaction kinetics; chemical kinetics; mathematical chemistry; catalysis; chemical engineering
Prof. Dr. Alexander N. Gorban

E-Mail Website
Guest Editor
Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK
Interests: neural networks; chemical and biological kinetics; human adaptation to hard living conditions; methods and technologies of collective thinking
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue will be devoted to the anniversary of thе book “Kinеtiс Modеls of Catalytic Rеactions” [1]. This book became a significant milestone in the development of chemical kinetics of complex reactions and heterogeneous catalysis and, moreover, mathematical chemistry with a focus on revealing the detailed mechanism based on complex kinetic behavior. Most of results presented in the book were original, especially the relationships between thermodynamic and kinetic characteristics, the applications of the graph theory to complex chemical kinetics, the studies of non-steady-state and nonlinear kinetic phenomena, i.e., slow rеlaxation and critical retardation, bi-stability and oscillations, etc. As for the concrete kinetic models, oxidative catalytic reactions have been thoroughly analyzed, with CO oxidation over platinum being thе “Holy Grail” of hеtеrogеnous catalysis.

Prеsеntly, thirty yеars latеr, it makes sense to rеvisit the area and describe its progress in terms of approaches reported in this book, еspеcially for the analysis of the complexity of chemical reactions.

References

[1] Yablonsky, G.; Gorban, A.; Bykov, V.; Elokhin, V. Kinеtiс Modеls of Catalytic Rеactions; Elsevier: Amsterdam, The Netherlands, 1991; 442p.

Prof. Dr. Gregory Yablonsky
Prof. Dr. Alexander N. Gorban
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

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Keywords

  • heterogeneous catalysis
  • chemical kinetics
  • complexity in chemical kinetics
  • graph theory in chemical kinetics
  • chemical kinetics and thermodynamics
  • non-steady-state chemical kinetics
  • chemical relaxation
  • temporal analysis of products (TAP)
  • non-linearity in chemical kinetics
  • critical phenomena in chemical kinetics
  • oscillations and multiplicity in chemistry
  • catalyst deactivation

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Published Papers (1 paper)

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Review

45 pages, 7545 KiB  
Review
Hamiltonian Computational Chemistry: Geometrical Structures in Chemical Dynamics and Kinetics
by Stavros C. Farantos
Entropy 2024, 26(5), 399; https://doi.org/10.3390/e26050399 - 30 Apr 2024
Viewed by 1818
Abstract
The common geometrical (symplectic) structures of classical mechanics, quantum mechanics, and classical thermodynamics are unveiled with three pictures. These cardinal theories, mainly at the non-relativistic approximation, are the cornerstones for studying chemical dynamics and chemical kinetics. Working in extended phase spaces, we show [...] Read more.
The common geometrical (symplectic) structures of classical mechanics, quantum mechanics, and classical thermodynamics are unveiled with three pictures. These cardinal theories, mainly at the non-relativistic approximation, are the cornerstones for studying chemical dynamics and chemical kinetics. Working in extended phase spaces, we show that the physical states of integrable dynamical systems are depicted by Lagrangian submanifolds embedded in phase space. Observable quantities are calculated by properly transforming the extended phase space onto a reduced space, and trajectories are integrated by solving Hamilton’s equations of motion. After defining a Riemannian metric, we can also estimate the length between two states. Local constants of motion are investigated by integrating Jacobi fields and solving the variational linear equations. Diagonalizing the symplectic fundamental matrix, eigenvalues equal to one reveal the number of constants of motion. For conservative systems, geometrical quantum mechanics has proved that solving the Schrödinger equation in extended Hilbert space, which incorporates the quantum phase, is equivalent to solving Hamilton’s equations in the projective Hilbert space. In classical thermodynamics, we take entropy and energy as canonical variables to construct the extended phase space and to represent the Lagrangian submanifold. Hamilton’s and variational equations are written and solved in the same fashion as in classical mechanics. Solvers based on high-order finite differences for numerically solving Hamilton’s, variational, and Schrödinger equations are described. Employing the Hénon–Heiles two-dimensional nonlinear model, representative results for time-dependent, quantum, and dissipative macroscopic systems are shown to illustrate concepts and methods. High-order finite-difference algorithms, despite their accuracy in low-dimensional systems, require substantial computer resources when they are applied to systems with many degrees of freedom, such as polyatomic molecules. We discuss recent research progress in employing Hamiltonian neural networks for solving Hamilton’s equations. It turns out that Hamiltonian geometry, shared with all physical theories, yields the necessary and sufficient conditions for the mutual assistance of humans and machines in deep-learning processes. Full article
(This article belongs to the Special Issue Kinetic Models of Chemical Reactions)
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