Daan van de Weem | Searcharxiv

arXiv2026

Emergent conserved quantities via irreversibility

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.

cond-mat.stat-mech↗

arXiv2025

On data and dimension in chemistry -- irreversibility, concealment and emergent conservation laws

Chemical systems are interpreted through the species they contain and the reactions they may undergo, i.e., their chemical reaction network (CRN). In spite of their central importance to chemistry, the structure of CRNs continues to be challenging to deduce from data. Although there exist structural laws relating species, reactions, conserved quantities and cycles, there has been limited attention to their measurable consequences. One such is the dimension of the chemical data: the number of independent reactions or equivalently independent species, which corresponds to the number of measured variables minus the number of constraints. In this paper we attempt to relate the experimentally observed dimensional features to conservation laws and underlying CRN structure. Our approach extends to any Markov model as well as many nonlinear models in statistical physics and furnishes new analytical tools to find exact solutions. In particular, we investigate the effects of species that are concealed and reactions that are irreversible. For instance, irreversible reactions can have proportional rates. The resulting reduction in degrees of freedom can be captured by the co-production law relating co-production relationships to emergent non-integer conservation laws and broken cycles. This law resolves a recent conundrum posed by a machine-discovered candidate for a non-integer conservation law, and characterizes certain types of CRN behavior. We also obtain laws that allow us to relate data dimension to network structure in cases where some species cannot be discerned or distinguished by a given analytical technique, allowing to narrow down candidate CRNs from experimental data more effectively.

cond-mat.stat-mech↗