A historical note on the entropy principle of Muller and Liu
In rational thermodynamics, the entropy principle of Müller and Liu is an important tool for deriving restrictions on the a priori unknown constitutive relations between the basic fields on the body under investigation and the material-specific physical quantities which enter the field equations. A...
| Main Authors: | , |
|---|---|
| Format: | Journal article |
| Language: | English |
| Published: |
2002
|
| _version_ | 1797099144459845632 |
|---|---|
| author | Hauser, R Kirchner, N |
| author_facet | Hauser, R Kirchner, N |
| author_sort | Hauser, R |
| collection | OXFORD |
| description | In rational thermodynamics, the entropy principle of Müller and Liu is an important tool for deriving restrictions on the a priori unknown constitutive relations between the basic fields on the body under investigation and the material-specific physical quantities which enter the field equations. A central role in this approach is played by a lemma of Liu which gives necessary and sufficient conditions for a linear inequality on a finite-dimensional space to be implied by a given finite set of linear equalities. We point out that this lemma is a special case of a well-known classical result by Farkas and Minkowski related to the duality theory of linear programming and to separation theorems such as e.g. the Hahn-Banach theorem of functional analysis. |
| first_indexed | 2024-03-07T05:19:29Z |
| format | Journal article |
| id | oxford-uuid:de614f1f-7aa5-4325-819f-f60e70665607 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:19:29Z |
| publishDate | 2002 |
| record_format | dspace |
| spelling | oxford-uuid:de614f1f-7aa5-4325-819f-f60e706656072022-03-27T09:31:52ZA historical note on the entropy principle of Muller and LiuJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:de614f1f-7aa5-4325-819f-f60e70665607EnglishSymplectic Elements at Oxford2002Hauser, RKirchner, NIn rational thermodynamics, the entropy principle of Müller and Liu is an important tool for deriving restrictions on the a priori unknown constitutive relations between the basic fields on the body under investigation and the material-specific physical quantities which enter the field equations. A central role in this approach is played by a lemma of Liu which gives necessary and sufficient conditions for a linear inequality on a finite-dimensional space to be implied by a given finite set of linear equalities. We point out that this lemma is a special case of a well-known classical result by Farkas and Minkowski related to the duality theory of linear programming and to separation theorems such as e.g. the Hahn-Banach theorem of functional analysis. |
| spellingShingle | Hauser, R Kirchner, N A historical note on the entropy principle of Muller and Liu |
| title | A historical note on the entropy principle of Muller and Liu |
| title_full | A historical note on the entropy principle of Muller and Liu |
| title_fullStr | A historical note on the entropy principle of Muller and Liu |
| title_full_unstemmed | A historical note on the entropy principle of Muller and Liu |
| title_short | A historical note on the entropy principle of Muller and Liu |
| title_sort | historical note on the entropy principle of muller and liu |
| work_keys_str_mv | AT hauserr ahistoricalnoteontheentropyprincipleofmullerandliu AT kirchnern ahistoricalnoteontheentropyprincipleofmullerandliu AT hauserr historicalnoteontheentropyprincipleofmullerandliu AT kirchnern historicalnoteontheentropyprincipleofmullerandliu |