Next Article in Journal
Work Availability and Exergy Analysis
Next Article in Special Issue
Solving Stochastic Reaction Networks with Maximum Entropy Lagrange Multipliers
Previous Article in Journal
Thermodynamic Analysis of Irreversible Desiccant Systems
Article Menu
Issue 8 (August) cover image

Export Article

Open AccessArticle
Entropy 2018, 20(8), 596; https://doi.org/10.3390/e20080596

Gradient and GENERIC Systems in the Space of Fluxes, Applied to Reacting Particle Systems

Weierstrass Institute (WIAS), Mohrenstrasse 39, 10117 Berlin, Germany
Received: 2 July 2018 / Revised: 2 August 2018 / Accepted: 8 August 2018 / Published: 9 August 2018
Full-Text   |   PDF [442 KB, uploaded 17 August 2018]   |  

Abstract

In a previous work we devised a framework to derive generalised gradient systems for an evolution equation from the large deviations of an underlying microscopic system, in the spirit of the Onsager–Machlup relations. Of particular interest is the case where the microscopic system consists of random particles, and the macroscopic quantity is the empirical measure or concentration. In this work we take the particle flux as the macroscopic quantity, which is related to the concentration via a continuity equation. By a similar argument the large deviations can induce a generalised gradient or GENERIC system in the space of fluxes. In a general setting we study how flux gradient or GENERIC systems are related to gradient systems of concentrations. This shows that many gradient or GENERIC systems arise from an underlying gradient or GENERIC system where fluxes rather than densities are being driven by (free) energies. The arguments are explained by the example of reacting particle systems, which is later expanded to include spatial diffusion as well. View Full-Text
Keywords: large deviations; fluxes; macroscopic fluctuation theory; Onsager–Machlup; gradient structures; GENERIC; chemical reaction networks large deviations; fluxes; macroscopic fluctuation theory; Onsager–Machlup; gradient structures; GENERIC; chemical reaction networks
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Renger, D.R.M. Gradient and GENERIC Systems in the Space of Fluxes, Applied to Reacting Particle Systems. Entropy 2018, 20, 596.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

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