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 Cram\'{e}r--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.
Highlights
The history of chemical thermodynamics originates around the middle of the nineteenth century [1,2]
One of the most important results of chemical reaction network theory (CRNT) is that a class of chemical reaction networks called a complex balanced network has a Lyapunov function, which can be associated with thermodynamic quantities such as the Gibbs free energy [3,6,7]
We have studied thermodynamics of chemical reaction networks in terms of information geometry
Summary
The history of chemical thermodynamics originates around the middle of the nineteenth century [1,2]. One of the most important results of CRNT is that a class of chemical reaction networks called a complex balanced network has a Lyapunov function, which can be associated with thermodynamic quantities such as the Gibbs free energy [3,6,7]. This Lyapunov function is called the pseudo-Helmholtz function, and its time derivative is connected to the entropy production rate [8,9].
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
