Mixed Bose-Fermi statistics: kinetic equation and navigation through a network

Area of Science:

• Statistical Physics
• Complex Systems
• Network Science

Background:

• Conventional master equations describe system evolution but lack mixed statistics.
• Real-world systems like traffic and epidemics involve complex interactions and movement patterns.

Purpose of the Study:

• To generalize the master equation to include both Bose and Fermi moves.
• To investigate the impact of mixed statistics, controlled by an exploratory tendency (ET) factor, on system dynamics.
• To analyze navigation behavior in scale-free networks with varying numbers of participants.

Main Methods:

• Generalized the master equation to incorporate Bose and Fermi moves.
• Introduced a fraction of Fermi moves (α) as an exploratory tendency (ET) factor.
• Conducted numerical simulations of navigation through a model scale-free network.

Main Results:

• Observed diverse behavior scenarios based on ET factor and total participants (N(tot)).
• For N(tot)>>1, all participants reach a target state if α<1, but excessive detour intention (α→1) causes critical slowdown.
• When α=1 (solely Fermi moves), one participant reaches the target faster by optimizing their path at the expense of others.

Conclusions:

• The generalized master equation provides a framework for studying systems with mixed Bose-Fermi statistics.
• The exploratory tendency factor significantly influences collective navigation dynamics in networks.
• The approach offers insights into optimizing movement strategies in complex, multi-agent systems.