2025/07/31 by So Katagiri, Yoshiki Matsuoka, Katagiri, So +3 · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Axiom #Control and Stability of Dynamical Systems #Covariant transformation #Detailed balance #Dissipative system #Entropy (arrow of time) #Extended irreversible thermodynamics #Formalism (music) #Limit (mathematics) #Thermoelastic and Magnetoelastic Phenomena #cond-mat.stat-mech #hep-th #math-ph #math.MP
paper · pdf · doi:10.1063/5.0319731
published in Chaos An Interdisciplinary Journal of Nonlinear Science 36(7) (American Institute of Physics)
openalex publication_date 2026/07/01 · openalex created_date 2026/07/21 · openalex updated_date 2026/08/05
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.