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Quantifying Spatiotemporal Parameters of Cellular Exocytosis in Micropatterned Cells

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Large deviation function for the current in the open asymmetric simple exclusion process.

Jan de Gier¹, Fabian H L Essler

¹Department of Mathematics and Statistics, The University of Melbourne, Victoria, Australia.

Physical Review Letters

|July 30, 2011

Summary

This summary is machine-generated.

We studied particle flow in a one-dimensional system with boundary interactions. An exact formula for current statistics in the infinite system limit was conjectured, revealing insights into system dynamics.

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Area of Science:

Statistical Mechanics
Non-equilibrium Physics
Complex Systems

Background:

The asymmetric exclusion process is a fundamental model in statistical mechanics.
Understanding non-equilibrium systems with boundary conditions is crucial for various fields.
The model exhibits rich phase behavior, including four distinct stationary states.

Purpose of the Study:

To analyze the current statistics in the low and high density phases of the one-dimensional asymmetric exclusion process.
To investigate particle injection and extraction dynamics at system boundaries.
To derive an exact expression for the current large deviation function in the infinite system size limit.

Main Methods:

Analysis of current statistics at the first site of the system.
Focus on the low and high density phases.
Asymptotic analysis in the limit of infinite system size.

Main Results:

Detailed analysis of current fluctuations in specific phases.
Conjectured an exact expression for the current large deviation function.
Provided insights into the stationary state properties of the model.

Conclusions:

The study provides a significant step towards understanding the exact statistical properties of the asymmetric exclusion process.
The conjectured large deviation function offers a powerful tool for future research.
The findings contribute to the broader field of non-equilibrium statistical mechanics.