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Linearization of the Bradford Protein Assay

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Unified linear fluctuation-response theory arbitrarily far from equilibrium.

Jiming Zheng¹, Zhiyue Lu¹

¹University of North Carolina - Chapel Hill, Department of Chemistry, Chapel Hill, North Carolina 27599, USA.

Physical Review. E

|January 21, 2026

Summary

This study introduces a new physics framework to understand how systems respond to changes. It generalizes the fluctuation-dissipation theorem for complex, nonequilibrium systems, enabling efficient calculations from observed data.

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Area of Science:

Physics
Statistical Mechanics
Complex Systems

Background:

Understanding system responses to perturbations is crucial, especially for nonequilibrium and nonstationary processes.
The fluctuation-dissipation theorem applies to near-equilibrium systems, with recent bounds for specific nonequilibrium regimes.

Purpose of the Study:

To present a unified, trajectory-score-based formulation for linear fluctuation-response relations in arbitrary Markov processes.
To generalize and extend existing theories, including the fluctuation-dissipation theorem, to a broader range of systems.

Main Methods:

Developed a compact, trajectory-score-based formulation.
Decomposed system response into spatial correlations of local dynamical events.
Analyzed correlations between transitions and dwelling times across networks.

Main Results:

Synthesized and generalized linear fluctuation-response relations for arbitrary Markov processes.
Revealed that response properties are encoded in correlations between transitions and dwelling times.
Unified existing response bounds and extended them to time-dependent processes.

Conclusions:

The new framework provides a generalized fluctuation-dissipation theorem for nonequilibrium systems.
It enables efficient numerical evaluation of response properties from unperturbed trajectories.
Offers significant advantages for studying complex networks and biological systems far from equilibrium.