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Irreversibility and fluctuation theorem in stationary time series
A Porporato1, J R Rigby, E Daly
1Department of Civil and Environmental Engineering, Duke University, Durham, North Carolina, USA.
Physical Review Letters
|March 16, 2007
Summary
This study quantifies time asymmetry in stationary time series using relative entropy. It links signal asymmetry to distance from equilibrium and lack of detailed balance, drawing parallels with nonequilibrium thermodynamics.
Area of Science:
- Statistical physics
- Information theory
- Time series analysis
Background:
- Quantifying time irreversibility is crucial in analyzing complex systems.
- Stationary time series exhibit statistical properties that remain constant over time.
- Understanding deviations from equilibrium is fundamental in thermodynamics.
Purpose of the Study:
- To develop a method for quantifying time asymmetry in stationary time series.
- To establish a connection between time asymmetry and thermodynamic concepts like distance from equilibrium and detailed balance.
- To investigate the statistical properties of time asymmetry using fluctuation theorems.
Main Methods:
- Calculating the relative entropy between joint probability distributions of forward and backward sequences.
- Applying concepts from the thermodynamic theory of nonequilibrium steady states.
- Analyzing the statistics of time asymmetry through the lens of fluctuation theorems.
Main Results:
- Relative entropy effectively quantifies time asymmetry in stationary time series.
- A direct relationship is established between signal asymmetry, distance from equilibrium, and the lack of detailed balance.
- The study demonstrates that fluctuation theorems provide a general framework for understanding time asymmetry statistics.
Conclusions:
- Time asymmetry in stationary time series can be robustly quantified using relative entropy.
- The findings offer a novel perspective linking information-theoretic measures with thermodynamic principles.
- The derived statistical relationships for time asymmetry are universally applicable to stationary time series.
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