Abstract
We discuss a relationship between information geometry and the Glansdorff–Prigogine criterion for stability. For the linear master equation, we found a relation between the line element and the excess entropy production rate. This relation leads to a new perspective of stability in a nonequilibrium steady-state. We also generalize the Glansdorff–Prigogine criterion for stability based on information geometry. Our information-geometric criterion for stability works well for the nonlinear master equation, where the Glansdorff–Prigogine criterion for stability does not work well. We derive a trade-off relation among the fluctuation of the observable, the mean change of the observable, and the intrinsic speed. We also derive a novel thermodynamic trade-off relation between the excess entropy production rate and the intrinsic speed. These trade-off relations provide a physical interpretation of our information-geometric criterion for stability. We illustrate our information-geometric criterion for stability by an autocatalytic reaction model, where dynamics are driven by a nonlinear master equation.
Highlights
The behavior of the system around the nonequilibrium steady-state has been well discussed in nonequilibrium thermodynamics
We show that the excess entropy production rate is given by the time derivative of the Lyapunov candidate function for the linear master equation, and this Lyapunov candidate function is related to the square of the line element in information geometry
We introduce the setup of linear irreversible thermodynamics [10], which explains the behavior of the system under the near-equilibrium condition
Summary
The behavior of the system around the nonequilibrium steady-state has been well discussed in nonequilibrium thermodynamics. The concept of thermodynamic trade-off relations is similar to the Glansdorff-Prigogine criterion for stability because the excess entropy production rate decides the stability of the steady-state. We show that the excess entropy production rate is given by the time derivative of the Lyapunov candidate function for the linear master equation, and this Lyapunov candidate function is related to the square of the line element in information geometry. This relation gives a geometric interpretation of the Onsager matrix under the near-equilibrium condition. We illustrate the merit of our information-geometric criterion for stability by a model of autocatalytic reaction driven by a nonlinear master equation
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