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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.00207 |
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| _version_ | 1866913099910479872 |
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| author | Katagiri, So Matsuoka, Yoshiki Sugamoto, Akio |
| author_facet | Katagiri, So Matsuoka, Yoshiki Sugamoto, Akio |
| contents | We present a theoretical framework for non-equilibrium thermodynamics, termed Nambu Non-equilibrium Thermodynamics (NNET), which unifies reversible dynamics described by the Nambu bracket and irreversible processes driven by entropy gradients. The formulation provides a covariant description of systems far from equilibrium, where entropy may transiently decrease as a result of reversible circulations or exchanges with the surroundings, extending the applicability of conventional thermodynamic formalisms.
As an illustrative example, a triangular chemical reaction system is analyzed. It is shown that, without assuming detailed balance or linearity, two geometric structures that behave as conserved quantities in the reversible limit naturally emerge: one associated with cyclic symmetry in the reaction space, and another that vanishes under symmetric reaction rates. These results demonstrate that NNET provides a unified and covariant formulation for describing both cyclic dynamics and dissipative processes within a single theoretical structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00207 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nambu Non-equilibrium Thermodynamics: Axiomatic Formulation and Foundation Katagiri, So Matsuoka, Yoshiki Sugamoto, Akio Statistical Mechanics High Energy Physics - Theory Mathematical Physics 82C05, 37N25, 70H33, 37J30, 80A20 We present a theoretical framework for non-equilibrium thermodynamics, termed Nambu Non-equilibrium Thermodynamics (NNET), which unifies reversible dynamics described by the Nambu bracket and irreversible processes driven by entropy gradients. The formulation provides a covariant description of systems far from equilibrium, where entropy may transiently decrease as a result of reversible circulations or exchanges with the surroundings, extending the applicability of conventional thermodynamic formalisms. As an illustrative example, a triangular chemical reaction system is analyzed. It is shown that, without assuming detailed balance or linearity, two geometric structures that behave as conserved quantities in the reversible limit naturally emerge: one associated with cyclic symmetry in the reaction space, and another that vanishes under symmetric reaction rates. These results demonstrate that NNET provides a unified and covariant formulation for describing both cyclic dynamics and dissipative processes within a single theoretical structure. |
| title | Nambu Non-equilibrium Thermodynamics: Axiomatic Formulation and Foundation |
| topic | Statistical Mechanics High Energy Physics - Theory Mathematical Physics 82C05, 37N25, 70H33, 37J30, 80A20 |
| url | https://arxiv.org/abs/2508.00207 |