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

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.

Added an appendix on entropy production and linear stability in Nambu Non-equilibrium Thermodynamics. Minor clarifications were made. Main results are unchanged. (30 pages)