Applications of Nambu Non-equilibrium Thermodynamics to Specific Phenomena

So Katagiri; Yoshiki Matsuoka; Akio Sugamoto

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arXiv · 2509.12641

Applications of Nambu Non-equilibrium Thermodynamics to Specific Phenomena

So Katagiri·Yoshiki Matsuoka·Akio Sugamoto

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Abstract

We apply Nambu non-equilibrium thermodynamics (NNET), a dynamics with multiple Hamiltonians coupled to entropy-induced dissipation, to paradigmatic far-from-equilibrium systems. Concretely, we construct NNET realizations for the Belousov-Zhabotinsky (BZ) reaction (oscillatory), the Hindmarsh-Rose neuron model (spiking), and the Lorenz and Chen systems (chaotic), and analyze their dynamical and thermodynamic signatures. Across all cases the velocity field cleanly decomposes into a non-dissipative Nambu part and a dissipative entropy-gradient part, anchored by a model-independent quasi-conserved quantity. This construction reproduces cycles, spikes, and strange-attractor behavior. These results demonstrate that NNET provides a unified, quantitatively consistent framework for oscillatory, spiking, and chaotic non-equilibrium systems, offering a systematic description beyond the Onsager-type near-equilibrium linear-response framework and complementary to nonlinear geometric formulations such as GENERIC.

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So Katagiri, Yoshiki Matsuoka, Akio Sugamoto. 2025-09-16. Applications of Nambu Non-equilibrium Thermodynamics to Specific Phenomena. https://arxiv.org/abs/2509.12641

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