How the Hahn-Banach Theorem Sheds Bright Light on Fundamental Questions in Classical Thermodynamics
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914547297681408 |
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| author | Feinberg, Martin Lavine, Richard B. |
| author_facet | Feinberg, Martin Lavine, Richard B. |
| contents | The Hahn-Banach Theorem, a cornerstone of modern functional analysis, is a natural companion of the Second Law of Thermodynamics. From a Kelvin-Planck version of the Second Law, the Hahn-Banach Theorem delivers, immediately and simultaneously, entropy and thermodynamic-temperature functions of the local material state such that the Clausius-Duhem inequality is satisfied for every process a particular material might admit. For \emph{existence} of such functions there is no need at all to require that their domain be restricted to states of equilibrium. However, the Hahn-Banach Theorem also indicates that for \emph{uniqueness} of such a pair of functions across the entire state-space domain, every state must be visited by a reversible process. This review is intended to help make accessible to both thermodynamics scholars and mathematicians the remarkable interplay of the Hahn-Banach Theorem and the Second Law. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22717 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | How the Hahn-Banach Theorem Sheds Bright Light on Fundamental Questions in Classical Thermodynamics Feinberg, Martin Lavine, Richard B. Classical Physics Mathematical Physics Dynamical Systems Functional Analysis Chemical Physics The Hahn-Banach Theorem, a cornerstone of modern functional analysis, is a natural companion of the Second Law of Thermodynamics. From a Kelvin-Planck version of the Second Law, the Hahn-Banach Theorem delivers, immediately and simultaneously, entropy and thermodynamic-temperature functions of the local material state such that the Clausius-Duhem inequality is satisfied for every process a particular material might admit. For \emph{existence} of such functions there is no need at all to require that their domain be restricted to states of equilibrium. However, the Hahn-Banach Theorem also indicates that for \emph{uniqueness} of such a pair of functions across the entire state-space domain, every state must be visited by a reversible process. This review is intended to help make accessible to both thermodynamics scholars and mathematicians the remarkable interplay of the Hahn-Banach Theorem and the Second Law. |
| title | How the Hahn-Banach Theorem Sheds Bright Light on Fundamental Questions in Classical Thermodynamics |
| topic | Classical Physics Mathematical Physics Dynamical Systems Functional Analysis Chemical Physics |
| url | https://arxiv.org/abs/2604.22717 |