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Linear Response and Fluctuation-Dissipation Relations for Brownian Motion under Resetting.
1Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, D-12489 Berlin, Germany and IRIS Adlershof, Humboldt-Universität zu Berlin, Zum Großen Windkanal 6, D-12489 Berlin, Germany.
Physical Review Letters
|February 24, 2023
Summary
This study examines fluctuation-dissipation relations (FDRs) in Brownian motion with renewal resetting. It finds that even when standard FDRs fail, a generalized Einstein
Area of Science:
- Statistical Mechanics
- Non-equilibrium Physics
- Brownian Motion
Background:
- Brownian motion is a fundamental model in statistical mechanics.
- Renewal resetting introduces non-Markovian dynamics.
- Fluctuation-Dissipation Relations (FDRs) connect system response to equilibrium fluctuations.
Purpose of the Study:
- To investigate the validity of FDRs and generalized Einstein's relations (GER) for Brownian motion under renewal resetting.
- To analyze how different waiting time distributions affect these relations.
- To determine the effective temperature in such non-equilibrium systems.
Main Methods:
- Analysis of fluctuation-dissipation relations (FDRs).
- Consideration of generalized Einstein's relations (GER).
- Mathematical treatment of arbitrary waiting time distributions in renewal resetting processes.
Main Results:
- Standard FDRs and GER apply when the waiting time distribution has a second moment.
- When the second moment diverges but the first moment is finite, static susceptibility diverges, standard FDRs break down, but GER remains valid.
- In all considered cases, FDRs indicate an effective temperature twice that of the medium.
Conclusions:
- The generalized Einstein's relation (GER) offers a robust framework for describing Brownian motion with renewal resetting, even when standard FDRs fail.
- The effective temperature of the system is consistently twice the medium's temperature, irrespective of the waiting time distribution's properties.
- This work provides insights into non-equilibrium statistical mechanics and the behavior of systems with intermittent dynamics.
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