Emergent conserved quantities via irreversibility

TL;DR

This paper reveals how irreversibility in chemical reaction networks and Markov chains leads to emergent conservation laws and broken cycles, providing new tools for model inference.

Contribution

It introduces a novel interpretation of recently discovered conserved quantities as emergent laws due to irreversibility, extending existing index laws.

Findings

Irreversible reactions cause emergent conservation laws.

Broken cycles are linked to linearly dependent currents.

A law relating conserved quantities, broken cycles, and co-production is derived.

Abstract

Conserved quantities increasingly underpin the inference of physical models. Recently new conserved quantities have been found in this context, that currently lack an interpretation. Here, we show that irreversible reactions in CRNs and Markov Chains lead to emergent conservation laws and broken cycles. Linearly dependent currents - characterized by the "co-production index" - arise due to irreversible reactions. We derive a law relating conserved quantities, broken cycles, and co-production. This resolves a recent conundrum posed by a machine-discovered candidate for a non-integer conservation law. Our findings introduce heretofore overlooked extensions to a widely used index law for CRNs and Markov Chains that undercounts conservation laws. This furnishes new tools and immediate applications for the inference and analysis of models based on conservation laws.