Bridge, Reverse Bridge, and Their Control
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View abstract on PubMed
Summary
This summary is machine-generated.We studied time-reversal symmetry in stochastic process bridges, finding that some non-equilibrium systems can exhibit perfect symmetry even when detailed balance is broken. This reveals new insights into out-of-equilibrium dynamics.
Area Of Science
- Statistical physics
- Non-equilibrium thermodynamics
- Stochastic processes
Background
- The bridge problem in stochastic processes analyzes trajectories with fixed start and end points.
- Time-reversal symmetry is a key property, questioning if statistical properties are invariant under time reversal (t → τ-t).
- Investigating symmetry in systems violating detailed balance is crucial for understanding non-equilibrium dynamics.
Purpose Of The Study
- To derive a local condition for time-reversal asymmetry specifically for stochastic bridges.
- To explore conditions under which bridges can be time-reversal symmetric, even when the underlying process violates detailed balance.
- To quantify bridge asymmetry and its utility in analyzing out-of-equilibrium dynamics.
Main Methods
- Comparison of stochastic differential equations for the bridge and its time-reversed counterpart, derived via Doob's transform or stochastic optimal control.
- Derivation of a necessary condition for time-reversal symmetry involving current velocity and detailed balance.
- Analysis of a minimal non-equilibrium model (Brownian Gyrators) and its transformation into polar coordinates.
Main Results
- A necessary condition for time-reversal symmetry was derived, confirming symmetry when detailed balance holds.
- The study found that bridges can exhibit symmetry even if the underlying process breaks detailed balance.
- An example of partial symmetry was presented in Brownian Gyrators, and perfect symmetry was demonstrated for the squared modulus of a transformed Brownian Gyrator model.
Conclusions
- Stochastic bridges can display time-reversal symmetry under conditions where the original process does not satisfy detailed balance.
- The derived condition provides a framework for identifying and quantifying time-reversal asymmetry in bridges.
- The findings highlight the nuanced behavior of non-equilibrium systems and offer methods for analyzing their dynamics.
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