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Inflow rate, a time-symmetric observable obeying fluctuation relations.
Marco Baiesi1,2, Gianmaria Falasco3
1Department of Physics and Astronomy, University of Padova, Via Marzolo 8, I-35131 Padova, Italy.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 14, 2015
Summary
This study explores fluctuation relations for time-symmetric quantities in mesoscopic systems. We found new relations for inflow rate, connecting deterministic and stochastic dynamics.
Area of Science:
- Statistical Mechanics
- Non-equilibrium Thermodynamics
- Stochastic Processes
Background:
- Fluctuation theorems typically focus on entropy changes.
- Time-symmetric observables are less commonly studied in fluctuation relations.
- Understanding irreversibility in stochastic systems is crucial.
Purpose of the Study:
- To investigate fluctuation relations for time-symmetric quantities.
- To establish connections between deterministic and stochastic dynamics.
- To generalize fluctuation theorems beyond entropy production.
Main Methods:
- Analysis of mesoscopic jump systems.
- Derivation of detailed and integral fluctuation relations.
- Examination of the time-integrated difference between entrance and escape rates.
Main Results:
- Detailed and integral fluctuation relations were found for the inflow rate (time-integrated difference between entrance and escape rates).
- The inflow rate is time-symmetric and equivalent to phase-space contraction rate in discrete states.
- A formal connection was established between reversible deterministic systems and irreversible stochastic systems.
Conclusions:
- Fluctuation theorems can be extended to time-symmetric quantities.
- The inflow rate serves as a bridge between deterministic and stochastic descriptions.
- Fluctuation theorems are robust and largely independent of specific dynamic details.
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