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We discuss a relationship between information geometry and theGlansdorff-Prigogine criterion for stability. For the linear master equation,we found a relation between the line element and the excess entropy productionrate. This relation leads to a new perspective of stability in a nonequilibriumsteady-state. We also generalize the Glansdorff-Prigogine criterion forstability based on information geometry. Our information-geometric criterionfor stability works well for the nonlinear master equation, where theGlansdorff-Prigogine criterion for stability does not work well. We derive atrade-off relation among the fluctuation of the observable, the mean change ofthe observable, and the intrinsic speed. We also derive a novel thermodynamictrade-off relation between the excess entropy production rate and the intrinsicspeed. These trade-off relations provide a physical interpretation of ourinformation-geometric criterion for stability. We illustrate ourinformation-geometric criterion for stability by an autocatalytic reactionmodel, where dynamics are driven by a nonlinear master equation.

Information geometry, trade-off relations, and generalized Glansdorff-Prigogine criterion for stability