Exit probability in inflow dynamics: nonuniversality induced by range, asymmetry, and fluctuation

Area of Science:

• Statistical Mechanics
• Complex Systems
• Dynamical Models

Background:

• Existing one-dimensional dynamical models present challenges in understanding exit probability (EP).
• Systems with Ising spins evolving towards absorbing states are common in statistical physics.
• Information flow direction significantly impacts system dynamics.

Purpose of the Study:

• To investigate the exit probability (EP) in one-dimensional dynamical models with inward information flow.
• To determine the general form and influencing factors of EP in these models.
• To establish the nonuniversal behavior of EP and contrast it with outflow dynamics.

Main Methods:

• Analysis of one-dimensional dynamical models with Ising spins.
• Mathematical formulation of exit probability (EP) as a function of initial spin fraction.
• Examination of the EP exponent's dependence on interaction range, model symmetry, and fluctuations.

Main Results:

• The exit probability (EP) follows the general form E(x)=xα/xα+(1-x)α.
• The EP exponent (α) is sensitive to interaction range (r), model symmetry, and fluctuations.
• Nonlinear EP forms and varying α values were observed even in nearest-neighbor models, confirming nonuniversal behavior.

Conclusions:

• Exit probability (EP) in these inward-flowing dynamical systems exhibits nonuniversal behavior.
• Factors like interaction range, symmetry, and fluctuations critically determine the EP exponent.
• Distinguishing between inward and outward information flow dynamics is crucial for understanding system behavior.