A generalization of the Glansdorff-Prigogine criterion for stability based on information geometry and thermodynamic uncertainty relationships*

To consider the relationship between the excess entropy production and the Fisher information of time, we have generalized the Glansdorff-Prigogine criterion for stability. In information geometry, the Fisher information of time is the speed of a statistical manifold, and then our generalized criterion can be interpreted as a criterion by acceleration (deceleration) of this speed. If this speed is accelerated (decelerated), dynamics is unstable (stable).

Our generalization does work even for chemical kinetics driven by the non-linear master equation (e.g., the autocatalytic reaction), where the Glansdorff-Prigogine criterion does not work well. Moreover, our generalization is connected to the recent progress of thermodynamic uncertainty relationships (TURs), and we can quantitatively discuss the stability of dynamics based on TURs.