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Nambu non-equilibrium thermodynamics: Axiomatic formulation and foundation
So Katagiri1,2, Yoshiki Matsuoka1, Akio Sugamoto3
1Nature and Environment, Faculty of Liberal Arts, The Open University of Japan, Chiba 261-8586, Japan.
Chaos (Woodbury, N.Y.)
|July 20, 2026
Summary
Nambu Non-equilibrium Thermodynamics (NNET) unifies reversible and irreversible processes. This new framework offers a covariant description for systems far from equilibrium, revealing conserved quantities in chemical reactions.
Area of Science:
- Thermodynamics
- Theoretical Physics
- Chemical Kinetics
Background:
- Conventional thermodynamic formalisms struggle with systems far from equilibrium.
- Understanding non-equilibrium dynamics is crucial for various scientific fields.
Purpose of the Study:
- To introduce Nambu Non-equilibrium Thermodynamics (NNET), a unified theoretical framework.
- To provide a covariant description for systems far from equilibrium.
- To demonstrate the framework's applicability using a chemical reaction system.
Main Methods:
- Developed a theoretical framework unifying Nambu bracket dynamics and entropy gradients.
- Formulated a covariant description for non-equilibrium systems.
- Analyzed a triangular chemical reaction system without assuming detailed balance or linearity.
Main Results:
- NNET successfully unifies reversible and irreversible thermodynamic processes.
- The framework allows for transient entropy decrease in systems far from equilibrium.
- Identified two geometric conserved quantities in a chemical reaction system: one related to cyclic symmetry and another vanishing under symmetric rates.
Conclusions:
- NNET offers a unified and covariant approach to non-equilibrium thermodynamics.
- The framework extends the applicability of conventional thermodynamic theories.
- NNET provides insights into the interplay of cyclic dynamics and dissipative processes.
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