Totally asymmetric simple exclusion process with local resetting in a resource-constrained environment

Area of Science:

• Statistical Mechanics
• Non-equilibrium Physics
• Biophysics

Background:

• mRNA translation involves stochastic degradation, often modeled by resetting dynamics.
• Understanding particle transport in constrained environments is crucial for various physical and biological systems.

Purpose of the Study:

• To investigate an open totally asymmetric simple exclusion process with local resetting in a resource-constrained setting.
• To analyze the impact of resource limitations and resetting rates on system dynamics and phase behavior.

Main Methods:

• Utilized mean-field approximations to derive stationary state properties.
• Employed Monte Carlo simulations to validate theoretical predictions.
• Analyzed density profiles, phase diagrams, and shock dynamics.

Main Results:

• Identified a low-density-high-density phase separation unique to this open, resource-constrained system.
• Observed two distinct phase transitions for smaller filling factors, altering phase diagram topology.
• Demonstrated agreement between mean-field results and simulations.

Conclusions:

• Resource constraints significantly influence the phase behavior of exclusion processes with resetting.
• The resetting rate and finite-size effects play critical roles in shock dynamics.
• This model provides insights into mRNA translation and other complex systems.