Applications of Nambu Non-equilibrium Thermodynamics to Specific Phenomena

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.

39 pages and 27 figures, v2 This paper has undergone a comprehensive revision to enhance its overall clarity, coherence, and readability for the reader, v3, v4, v5 added some explanations, v6 updated the references, v7 added some explanations, figures, and references, v8 organized wordings and contents