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Dynamical phase transitions in certain nonergodic stochastic processes
Yogeesh Reddy Yerrababu1,2, Satya N Majumdar3, Benjamin Guiselin4
1University of Italian Switzerland, 6900 Lugano, Switzerland.
Physical Review. E
|July 24, 2026
Summary
Singularities in large deviation functions reveal dynamical phase transitions in stochastic processes. This study explores these transitions in Brownian motion and Markov chains, offering insights into complex system dynamics.
Area of Science:
- Statistical Physics
- Non-equilibrium Systems
- Stochastic Processes
Background:
- Large deviation functions (LDFs) characterize rare events in stochastic processes.
- Dynamical phase transitions describe abrupt changes in trajectory behavior.
- Understanding these phenomena is crucial for complex systems.
Purpose of the Study:
- To investigate singularities in LDFs of time-integrated observables.
- To connect these singularities to dynamical phase transitions in trajectories.
- To explore the generalizability of these findings.
Main Methods:
- Backward Fokker-Planck approach to derive LDFs for observables like displacement and residence time.
- Analysis using tilted operators to study effective dynamics at singular points.
- Rare-event simulation techniques for empirical validation.
Main Results:
- Singularities in LDFs emerge from the interplay between survival and diffusion.
- Abrupt transitions in effective dynamics observed at singular points.
- Generalizability shown for Markov chains, non-Markovian dynamics, and many-body systems.
Conclusions:
- Singular LDFs provide a powerful tool to identify and understand dynamical phase transitions.
- The framework is robust and applicable to a wide range of complex systems.
- Potential for discovering multiple dynamical phase transitions in various physical scenarios.
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