Fluctuation-response inequality out of equilibrium

Area of Science:

• Statistical Mechanics
• Information Theory
• Non-equilibrium Physics

Background:

• Understanding out-of-equilibrium systems is crucial in physics.
• Linear response theory describes system behavior under small perturbations.
• Information theory provides tools to quantify information flow and uncertainty.

Purpose of the Study:

• To develop a fluctuation-response inequality (FRI) for arbitrary out-of-equilibrium states.
• To connect linear response theory with information-theoretic concepts.
• To derive generalized uncertainty relations for stochastic dynamics.

Main Methods:

• Analyzing the response of an observable to perturbations in stochastic dynamics.
• Utilizing Kullback-Leibler divergence and relative entropy.
• Applying the FRI to steady-state particle transport and deriving generalized uncertainty relations.

Main Results:

• The magnitude of response is bounded by fluctuations and Kullback-Leibler divergence.
• Established a connection between linear response and information theory.
• Derived bounds for differential mobility in terms of diffusivity.
• Recovered the thermodynamic uncertainty relation (TUR) for steady-state transport.
• Generalized the TUR to arbitrary dynamics involving higher-order cumulants.

Conclusions:

• The developed FRI provides a fundamental link between statistical mechanics and information theory.
• The generalized uncertainty relation offers broader applicability beyond equilibrium and steady-state systems.
• The findings have implications for understanding and quantifying fluctuations in complex systems.