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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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Fluctuation-Response Inequalities for Kinetic and Entropic Perturbations.

Euijoon Kwon^1,2, Hyun-Myung Chun², Hyunggyu Park³

¹Seoul National University, Department of Physics and Astronomy and Center for Theoretical Physics, Seoul 08826, Republic of Korea.

Physical Review Letters

|September 15, 2025

Summary

This study introduces fluctuation-response inequalities for Markov jump processes, linking observable fluctuations to system responses. These new inequalities apply to more observables and finite times, including quantum systems.

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Area of Science:

Statistical Mechanics
Quantum Thermodynamics
Non-equilibrium Physics

Background:

Markov jump processes are fundamental to modeling dynamic systems.
Existing fluctuation-response relations often have limitations in applicability.
Understanding the relationship between fluctuations and responses is crucial in non-equilibrium systems.

Purpose of the Study:

To derive novel fluctuation-response inequalities for Markov jump processes.
To extend the applicability of fluctuation-response relations to a broader class of observables and finite observation times.
To investigate these inequalities in the context of open quantum systems.

Main Methods:

Derivation using the Cramér-Rao bound.
Application to general observables beyond current-like ones.
Extension to open quantum systems via the Lindblad quantum master equation.

Main Results:

Established fluctuation-response inequalities for Markov jump processes.
Demonstrated broader applicability compared to existing relations, including finite observation times.
Derived a quantum fluctuation-response inequality highlighting the role of dynamical activity.

Conclusions:

The derived inequalities provide a unified framework for understanding fluctuation-response relationships.
The findings offer a more general approach applicable to diverse systems, including quantum ones.
Dynamical activity is identified as a key factor in quantum fluctuation-response phenomena.