Classical stochastic systems with fast-switching environments: Reduced master equations, their interpretation, and...

Area of Science:

• Statistical Physics
• Stochastic Processes
• Non-equilibrium Systems

Background:

• Classical Markovian stochastic systems are often studied in isolation.
• Coupling systems to randomly switching environments introduces complexity.
• Adiabatic approximations simplify dynamics but neglect important corrections.

Purpose of the Study:

• To derive reduced dynamics for systems coupled to fast environmental fluctuations.
• To investigate corrections beyond the adiabatic limit.
• To analyze the implications of these corrections, including potential negative transition rates.

Main Methods:

• Derivation of reduced dynamics for discrete-state Markovian systems.
• Analysis of fast environmental processes and timescale separation.
• Comparison with adiabatic approximations and Kramers-Moyal expansions.

Main Results:

• Reduced dynamics can exhibit bursting events.
• Negative transition rates may arise, causing unphysical short-time behavior.
• The reduced master equation offers improved description of stationary states compared to leading-order adiabatic calculations.

Conclusions:

• Fast environmental switching necessitates going beyond simple adiabatic approximations.
• The derived reduced dynamics provide a more accurate description of stationary states.
• A criterion for negative rates in two-state environmental systems is established.