Recent Advances in Conservation–Dissipation Formalism for Irreversible Processes
The main purpose of this review is to summarize the recent advances of the Conservation–Dissipation Formalism (CDF), a new way for constructing both thermodynamically compatible and mathematically stable and well-posed models for irreversible processes. The contents include but are not restricted to...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/11/1447 |
| _version_ | 1797510476663357440 |
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| author | Liangrong Peng Liu Hong |
| author_facet | Liangrong Peng Liu Hong |
| author_sort | Liangrong Peng |
| collection | DOAJ |
| description | The main purpose of this review is to summarize the recent advances of the Conservation–Dissipation Formalism (CDF), a new way for constructing both thermodynamically compatible and mathematically stable and well-posed models for irreversible processes. The contents include but are not restricted to the CDF’s physical motivations, mathematical foundations, formulations of several classical models in mathematical physics from master equations and Fokker–Planck equations to Boltzmann equations and quasi-linear Maxwell equations, as well as novel applications in the fields of non-Fourier heat conduction, non-Newtonian viscoelastic fluids, wave propagation/transportation in geophysics and neural science, soft matter physics, etc. Connections with other popular theories in the field of non-equilibrium thermodynamics are examined too. |
| first_indexed | 2024-03-10T05:32:02Z |
| format | Article |
| id | doaj.art-f78f606bc70d46978ac908a3b71b11f3 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T05:32:02Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-f78f606bc70d46978ac908a3b71b11f32023-11-22T23:15:06ZengMDPI AGEntropy1099-43002021-10-012311144710.3390/e23111447Recent Advances in Conservation–Dissipation Formalism for Irreversible ProcessesLiangrong Peng0Liu Hong1College of Mathematics and Data Science, Minjiang University, Fuzhou 350108, ChinaSchool of Mathematics, Sun Yat-sen University, Guangzhou 510275, ChinaThe main purpose of this review is to summarize the recent advances of the Conservation–Dissipation Formalism (CDF), a new way for constructing both thermodynamically compatible and mathematically stable and well-posed models for irreversible processes. The contents include but are not restricted to the CDF’s physical motivations, mathematical foundations, formulations of several classical models in mathematical physics from master equations and Fokker–Planck equations to Boltzmann equations and quasi-linear Maxwell equations, as well as novel applications in the fields of non-Fourier heat conduction, non-Newtonian viscoelastic fluids, wave propagation/transportation in geophysics and neural science, soft matter physics, etc. Connections with other popular theories in the field of non-equilibrium thermodynamics are examined too.https://www.mdpi.com/1099-4300/23/11/1447conservation–dissipation formalismnon-equilibrium thermodynamicshyperbolic PDEsviscoelastic fluidssoft matter physics |
| spellingShingle | Liangrong Peng Liu Hong Recent Advances in Conservation–Dissipation Formalism for Irreversible Processes Entropy conservation–dissipation formalism non-equilibrium thermodynamics hyperbolic PDEs viscoelastic fluids soft matter physics |
| title | Recent Advances in Conservation–Dissipation Formalism for Irreversible Processes |
| title_full | Recent Advances in Conservation–Dissipation Formalism for Irreversible Processes |
| title_fullStr | Recent Advances in Conservation–Dissipation Formalism for Irreversible Processes |
| title_full_unstemmed | Recent Advances in Conservation–Dissipation Formalism for Irreversible Processes |
| title_short | Recent Advances in Conservation–Dissipation Formalism for Irreversible Processes |
| title_sort | recent advances in conservation dissipation formalism for irreversible processes |
| topic | conservation–dissipation formalism non-equilibrium thermodynamics hyperbolic PDEs viscoelastic fluids soft matter physics |
| url | https://www.mdpi.com/1099-4300/23/11/1447 |
| work_keys_str_mv | AT liangrongpeng recentadvancesinconservationdissipationformalismforirreversibleprocesses AT liuhong recentadvancesinconservationdissipationformalismforirreversibleprocesses |