Information Geometric Inequalities of Chemical Thermodynamics

Abstract

We study a connection between chemical thermodynamics and information geometry. We clarify a relation between the Gibbs free energy of an ideal dilute solution and an information-geometric quantity called an $f$-divergence. From this relation, we derive information-geometric inequalities that give a speed limit for a changing rate of the Gibbs free energy and a general bound of chemical fluctuations. These information-geometric inequalities can be regarded as generalizations of the Cramér--Rao inequality for chemical reaction networks described by rate equations, where unnormalized concentration distributions are of importance rather than probability distributions. They hold true for damped oscillatory reaction networks and systems where the total concentration is not conserved so that the distribution cannot be normalized. We also formulate a trade-off relation between speed and time on a manifold of concentration distribution by using the geometrical structure induced by the $f$-divergence. Our results apply to both closed and open chemical reaction networks, thus they are widely useful for thermodynamic analysis of chemical systems from the viewpoint of information geometry.

16 pages, 9 figures

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• Trade-offs between number fluctuations and response in nonequilibrium chemical reaction networks
• Universal constraint on nonlinear population dynamics
• Energy Landscape Design Principle for Optimal Energy Harnessing by Catalytic Molecular Machines
• Energy and entropy on irreversible chemical reaction-diffusion systems with asymptotic stability
• Infinite variety of thermodynamic speed limits with general activities
• Deficiency, Kinetic Invertibility, and Catalysis in Stochastic Chemical Reaction Networks
• Thermodynamic role of main reaction pathway and multi-body information flow in membrane transport
• Information-geometric structure for chemical thermodynamics: An explicit construction of dual affine coordinates
• Stochastic thermodynamics of Fisher information
• Riemannian Geometry of Optimal Driving and Thermodynamic Length and its Application to Chemical Reaction Networks
• Information geometric bound on general chemical reaction networks
• What is a chemostat? Insights from hybrid dynamics and stochastic thermodynamics
• Coarse Graining Photo-Isomerization Reactions: Thermodynamic Consistency and Implications for Molecular Ratchets
• Refined Thermodynamic Uncertainty Relation for Chemical Reactions
• Information geometry of nonmonotonic quantum natural gradient