Information Geometry and Universal Bounds on Non-stationary Responsiveness of Markov Dynamics

Markov dynamics can effectively describe a wide range of thermodynamic and biological processes. Understanding how such systems respond to changes in environmental variables or external inputs is crucial for predicting and controlling their behaviors. This work presents a set of universal thermodynamic bounds on the responsiveness of any Markov system toward environmental changes. The systems of interest can be arbitrarily far from stationary state. The central element of this work is the introduction of information geometry on the manifold of probability distributions of stochastic trajectories. This work lays the foundation for understanding biological processes, engineering artificial systems, and exploring the fundamental principles governing complex systems far from equilibrium.