Nambu Non-equilibrium Thermodynamics: Axiomatic Formulation and Foundation
Abstract
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.
Cite
@article{arxiv.2508.00207,
title = {Nambu Non-equilibrium Thermodynamics: Axiomatic Formulation and Foundation},
author = {So Katagiri and Yoshiki Matsuoka and Akio Sugamoto},
journal= {arXiv preprint arXiv:2508.00207},
year = {2026}
}
Comments
v2: The title and Introduction have been substantially revised to better reflect the conceptual framework and scope of the paper. Minor editorial improvements were made throughout the text. The theoretical content and main results remain unchanged. v3: Appendix A added. v4: Added comments and clarifications throughout the manuscript (19 pages). Revised version submitted to Chaos