Reduction of complex dynamics in far-from-equilibrium systems: Nambu non-equilibrium thermodynamics

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. 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.