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Ergodic-nonergodic transition in a threshold system with feedback.

Boyoung Seo¹, Toyonori Munakata

¹Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan. byseo@amp.i.kyoto-u.c.jp

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 10, 2006

Summary

This study investigates a threshold system with feedback, revealing a nonequilibrium phase transition. Analyzing the distribution function clarifies the transition point and limitations of traditional order parameters.

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Area of Science:

Statistical Mechanics
Nonlinear Dynamics
Complex Systems

Background:

Threshold systems with feedback are crucial in various scientific fields.
Understanding nonequilibrium phase transitions is key to characterizing complex system dynamics.
Traditional analysis often relies on order parameters, which may have limitations.

Purpose of the Study:

To study a threshold system with feedback through the lens of an ergodic-nonergodic transition.
To investigate how changing the rate of input signal variation affects this transition.
To clarify the role and limitations of the self-consistent equation for the order parameter.

Main Methods:

Analysis of the time evolution of the distribution function.
Identifying the transition point by examining the distribution function dynamics.
Relating feedback strength to activation energy using statistical mechanics.

Main Results:

The ergodic-nonergodic transition was identified as a type of nonequilibrium phase transition.
Examining the distribution function provided a more comprehensive understanding than using only the order parameter.
The limitations of the self-consistent equation for the order parameter were elucidated.
Feedback strength was successfully related to activation energy.

Conclusions:

The distribution function provides a robust method for analyzing nonequilibrium phase transitions in feedback systems.
This approach offers deeper insights into system behavior compared to solely relying on order parameters.
The findings contribute to a statistical mechanical understanding of feedback mechanisms and their relation to energy barriers.