Information Geometric Inequalities of Chemical Thermodynamics

Abstract

We study a connection between chemical thermodynamics and information geometry. We clarify a relationship between the Gibbs free energy of an ideal dilute solution and an information-geometric quantity called an f -divergence. From this relationship, 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 oscillatory reaction networks and systems where the total concentration is not conserved so that the distribution cannot be normalized. Our results apply to both closed and open chemical reaction networks, so they are widely useful for thermodynamic analysis of chemical systems from the viewpoint of information geometry.

Energy and entropy on irreversible chemical reaction-diffusion systems with asymptotic stability

“…This method allows us to re-understand the interaction between flows and forces that, proceeding in the usual way for reversible reactions, would lead to very restricted conditions that do not allow some observable behaviors to be included [50]. For example, although traditional approaches certainly allow us to include irreversibility as a limit case [43,44], the detailed balance assumption leaves out most of the usual reactiondiffusion models that proceed, in general, following irreversible mechanisms [27].…”

“…Note that the reaction velocities include only forward reaction rates since the steps are irreversible. This means that the hypothesis used in other works [43,44], that all systems are to some extent reversible, is not necessary for our formalism.…”

Nonequilibrium Thermodynamics of Non-Ideal Chemical Reaction Networks

“…Also applications to chaotic CRNs have been considered [25]. Recently, the connections of the theory to information geometry has been investigated [26]. Furthermore, di erence strategies to maintain nonequilibrium regimes, like the use of nite chemostats [27] and serial transfers in closed reactors [28], have been explored.…”