Fluctuating Non-linear Non-equilibrium System in Terms of Nambu Thermodynamics

TL;DR

This paper introduces a generalized Nambu dynamics framework to describe far-from-equilibrium non-linear systems with fluctuations, exemplified by chemical oscillations like the BZ reaction, revealing periodic entropy evolution.

Contribution

It develops a novel Nambu thermodynamics approach to model non-equilibrium systems with fluctuations, extending the description to far-from-equilibrium cyclic reactions.

Findings

Nambu brackets effectively describe far-from-equilibrium reactions.

Entropy evolution can be periodic, with Hamiltonian effects suppressing entropy increase.

Chemical oscillations are modeled successfully using this framework.

Abstract

It is shown that the structure of non-equilibrium thermodynamic system far from equilibrium can be captured in terms of a generalized "Nambu dynamics", in the presence of fluctuation effects in non-equilibrium thermodynamics. Triangular reactions are examined in detail, and it is shown that Nambu brackets can be used to describe them even when they are far from equilibrium, such as with cycles. Time evolution of the non-equilibrium state using the Hamiltonian and entropy is analyzed and it is shown that the entropy evolution is periodic with the negative contribution caused by the Hamiltonian suppressing the increase caused by entropy. As concrete examples, chemical reaction systems with time oscillation, such as the Belousov-Zhabotinsky reaction (BZ reaction), Hindmarsh-Rose(H-R) mode, are examined.