Emergent conserved quantities via irreversibility

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.