Nambu Non-equilibrium Thermodynamics: Axiomatic Formulation and Foundation

TL;DR

This paper introduces Nambu Non-equilibrium Thermodynamics (NNET), a covariant framework unifying reversible and irreversible processes, extending thermodynamics to far-from-equilibrium systems with transient entropy decreases.

Contribution

It presents a novel axiomatic formulation that combines Nambu brackets with entropy-driven irreversibility, providing a unified description of non-equilibrium phenomena.

Findings

Identifies geometric conserved quantities in a chemical reaction system.

Shows the framework accommodates systems with transient entropy decrease.

Demonstrates the emergence of cyclic symmetry and dissipative structures.

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.