Next Article in Journal
Information Geometric Complexity of a Trivariate Gaussian Statistical Model
Next Article in Special Issue
Density Reconstructions with Errors in the Data
Previous Article in Journal
Maximum Power of Thermally and Electrically Coupled Thermoelectric Generators
Previous Article in Special Issue
A Maximum Entropy Approach to Assess Debonding in Honeycomb aluminum Plates
Article Menu

Export Article

Open AccessArticle
Entropy 2014, 16(6), 2904-2943; doi:10.3390/e16062904

Reaction Kinetics Path Based on Entropy Production Rate and Its Relevance to Low-Dimensional Manifolds

Department of Mechanical Engineering, Faculty of Science and Technology, Meijo University, Nagoya, Aichi 468-8502, Japan
Received: 22 December 2013 / Revised: 13 May 2014 / Accepted: 14 May 2014 / Published: 26 May 2014
(This article belongs to the Special Issue Maximum Entropy and Its Application)

Abstract

The equation that approximately traces the trajectory in the concentration phase space of chemical kinetics is derived based on the rate of entropy production. The equation coincides with the true chemical kinetics equation to first order in a variable that characterizes the degree of quasi-equilibrium for each reaction, and the equation approximates the trajectory along at least final part of one-dimensional (1-D) manifold of true chemical kinetics that reaches equilibrium in concentration phase space. Besides the 1-D manifold, each higher dimensional manifold of the trajectories given by the equation is an approximation to that of true chemical kinetics when the contour of the entropy production rate in the concentration phase space is not highly distorted, because the Jacobian and its eigenvectors for the equation are exactly the same as those of true chemical kinetics at equilibrium; however, the path or trajectory itself is not necessarily an approximation to that of true chemical kinetics in manifolds higher than 1-D. The equation is for the path of steepest descent that sufficiently accounts for the constraints inherent in chemical kinetics such as element conservation, whereas the simple steepest-descent-path formulation whose Jacobian is the Hessian of the entropy production rate cannot even approximately reproduce any part of the 1-D manifold of true chemical kinetics except for the special case where the eigenvector of the Hessian is nearly identical to that of the Jacobian of chemical kinetics.
Keywords: entropy production rate; chemically reacting systems; quasi-equilibrium; low-dimensional manifolds; element conservation; steepest descent; Jacobian; eigenvectors; Hessian; trajectory entropy production rate; chemically reacting systems; quasi-equilibrium; low-dimensional manifolds; element conservation; steepest descent; Jacobian; eigenvectors; Hessian; trajectory
Figures

This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Kojima, S. Reaction Kinetics Path Based on Entropy Production Rate and Its Relevance to Low-Dimensional Manifolds. Entropy 2014, 16, 2904-2943.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top