Gradient Dynamics and Entropy Production Maximization
-
Adam Janečka
and
Michal Pavelka
Abstract
We compare two methods for modeling dissipative processes, namely gradient dynamics and entropy production maximization. Both methods require similar physical inputs–-how energy (or entropy) is stored and how it is dissipated. Gradient dynamics describes irreversible evolution by means of dissipation potential and entropy, it automatically satisfies Onsager reciprocal relations as well as their nonlinear generalization (Maxwell–Onsager relations), and it has statistical interpretation. Entropy production maximization is based on knowledge of free energy (or another thermodynamic potential) and entropy production. It also leads to the linear Onsager reciprocal relations and it has proven successful in thermodynamics of complex materials. Both methods are thermodynamically sound as they ensure approach to equilibrium, and we compare them and discuss their advantages and shortcomings. In particular, conditions under which the two approaches coincide and are capable of providing the same constitutive relations are identified. Besides, a commonly used but not often mentioned step in the entropy production maximization is pinpointed and the condition of incompressibility is incorporated into gradient dynamics.
Acknowledgements:
We are grateful to Oğul Esen for discussing the geometric origin of gradient dynamics and to Vít Pruša for discussing the method of entropy production maximization and for assistance during the review process.
This work was supported by Czech Science Foundation, project no. 17-15498Y.
Adam Janečka acknowledges the support of Project No. LL1202 in the programme ERC-CZ, funded by the Ministry of Education, Youth and Sports of the Czech Republic, and of Project 260 449/2017 “Student research in the field of physics didactics and mathematical and computer modelling”.
A k
A function is
Taking derivative with respect to
Taking derivative of eq. (73) with respect to
thus
When
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Articles in the same Issue
- Frontmatter
- Gradient Dynamics and Entropy Production Maximization
- Multiscale Transient and Steady-State Study of the Influence of Microstructure Degradation and Chromium Oxide Poisoning on Solid Oxide Fuel Cell Cathode Performance
- Fractional Effects on the Light Scattering Properties of a Simple Binary Mixture
- On Entropy Generation and the Effect of Heat and Mass Transfer Coupling in a Distillation Process
- Thermodynamic Analysis of TEG-TEC Device Including Influence of Thomson Effect
Articles in the same Issue
- Frontmatter
- Gradient Dynamics and Entropy Production Maximization
- Multiscale Transient and Steady-State Study of the Influence of Microstructure Degradation and Chromium Oxide Poisoning on Solid Oxide Fuel Cell Cathode Performance
- Fractional Effects on the Light Scattering Properties of a Simple Binary Mixture
- On Entropy Generation and the Effect of Heat and Mass Transfer Coupling in a Distillation Process
- Thermodynamic Analysis of TEG-TEC Device Including Influence of Thomson Effect
