Refined Thermodynamic Uncertainty Relation for Chemical Reactions

Abstract

Thermodynamic uncertainty relations elucidate the intricate balance between the precision of current and the thermodynamic costs or dissipation, marking a recent and enthralling advancement at the confluence of statistical mechanics, thermodynamics, and information theory. In this study, we derive a time-energy uncertainty relation tailored for chemical reactions, expressed in terms of the Gibbs free energy and chemical potential. This inequality holds true irrespective of whether the total substance of chemical species is conserved during the reaction. Furthermore, it supports the general thermodynamic framework by ensuring the spontaneous decrease in Gibbs free energy. We present two formulations of the thermodynamic uncertainty relation: one based on chemical species concentrations and the other on molar fractions. The validity of our inequalities is numerically demonstrated using model systems of the Belousov-Zhabotinsky and Michaelis-Menten reactions. Our uncertainty relation may find practical applications in measuring and optimizing thermodynamic properties relevant to chemical reaction systems out of equilibrium.

arXiv comment36 pages, 8 figures

References in corpus (15)

• Universal trade-off relation between power and efficiency for heat engines
• Quantifying dissipation using fluctuating currents
• Universal bound on the efficiency of molecular motors
• Thermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits
• Inferring entropy production from short experiments
• Unifying Thermodynamic Uncertainty Relations
• Time-information uncertainty relations in thermodynamics
• Improved bounds on entropy production in living systems
• Design principles for non-equilibrium self-assembly
• Unifying speed limit, thermodynamic uncertainty relation and Heisenberg principle via bulk-boundary correspondence
• Thermodynamic Uncertainty Relation Bounds the Extent of Anomalous Diffusion
• Information Geometric Inequalities of Chemical Thermodynamics
• Thermodynamic Uncertainty Relation in Interacting Many-Body Systems
• Thermodynamic Uncertainty Relations for Steady-State Thermodynamics
• Virial-like Thermodynamic Uncertainty Relation in the Tight-Binding Regime