Reduction of Complex Dynamics in Far-from-equilibrium Systems: Nambu Non-equilibrium Thermodynamics

TL;DR

This paper introduces a Nambu bracket-based framework to simplify and analyze complex far-from-equilibrium thermodynamic systems with strong nonlinearity, highlighting local reductions and challenges in global extension.

Contribution

It presents a novel reformulation of nonlinear non-equilibrium systems using Nambu brackets and proposes a generalized approach with higher-order tensors.

Findings

Complex systems can be locally reduced to Nambu Non-equilibrium Thermodynamics.

Mathematical obstacles in global reduction are identified and discussed.

A generalized formulation incorporating nonlinear effects is proposed.

Abstract

Far-from-equilibrium thermodynamic systems dominated by strong nonlinearity are reformulated within a dynamical framework based on the Nambu bracket formalism. It is demonstrated that general complex nonlinear non-equilibrium systems can be locally reduced to a simple form of Nambu Non-equilibrium Thermodynamics (NNET). Furthermore, mathematical and dynamical obstacles encountered in extending this reduction globally are discussed, and a generalized formulation that incorporates nonlinear effects through mixed higher-order tensors is proposed.