Does an irreversible chemical cycle support equilibrium?

TL;DR

This paper explores how irreversible chemical cycles can reach true equilibrium by redefining theoretical frameworks, avoiding divergence issues, and maintaining zero entropy production without detailed balance.

Contribution

It introduces a modified theoretical approach that allows irreversible cycles to attain equilibrium with zero entropy production, extending Onsager's framework.

Findings

Irreversible cycles can reach equilibrium with zero entropy production.

Redefinition of force terms avoids divergence in entropy production.

Equivalence with Onsager's theory is established for both reversible and irreversible cycles.

Abstract

The impossibility of attaining equilibrium for cyclic chemical reaction networks with irreversible steps is apparently due to a divergent entropy production rate. A deeper reason seems to be the violation of the detailed balance condition. In this work, we discuss how the standard theoretical framework can be adapted to include irreversible cycles, avoiding the divergence. With properly redefined force terms, such systems are also seen to reach and sustain equilibria that are characterized by the vanishing of the entropy production rate, though detailed balance is not maintained. Equivalence of the present formulation with Onsager's original prescription is established for both reversible and irreversible cycles, with a few adjustments in the latter case. Further justification of the attainment of true equilibrium is provided with the help of the minimum entropy production principle. All the results are generalized for an irreversible cycle comprising of N number of species.