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Nonequilibrium fluctuation-response relations for state observables
Krzysztof Ptaszyński1, Timur Aslyamov2, Massimiliano Esposito2
1Institute of Molecular Physics, Polish Academy of Sciences, Mariana Smoluchowskiego 17, 60-179 Poznań, Poland.
Physical Review. E
|March 20, 2026
Summary
We derived fluctuation-response relations for Markov jump processes, connecting system fluctuations to external perturbations. These findings establish bounds on state observable fluctuations and offer insights into their topological origins.
Area of Science:
- Non-equilibrium statistical mechanics
- Theoretical chemistry
- Physical chemistry
Background:
- Time-integrated state observables are crucial for understanding systems in chemical sensing and fluorescence spectroscopy.
- These observables quantify the system's time spent in specific states.
Purpose of the Study:
- To derive exact fluctuation-response relations for Markov jump processes in non-equilibrium steady states.
- To establish bounds on fluctuations of time-integrated state observables.
- To elucidate the mechanistic origin and topological dependence of these fluctuations.
Main Methods:
- Derivation of exact identities connecting fluctuations and responses.
- Analysis of Markov jump processes in non-equilibrium steady states.
- Application of fluctuation-response relations to derive bounds.
Main Results:
- Established fluctuation-response relations for time-integrated state observables.
- Derived upper and lower bounds on the fluctuations of these observables.
- Demonstrated that fluctuation properties depend solely on system topology.
Conclusions:
- The derived identities offer a deeper mechanistic understanding of fluctuations.
- Topological properties significantly influence fluctuation characteristics.
- These findings are relevant for model inference using experimental data, particularly in chemical sensing and spectroscopy.
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