Generalization of the Ehrenfest urn model to a complex network
Jaime Clark1, Miguel Kiwi1,2, Felipe Torres1,2
1Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, Chile.
Summary
This study extends the Ehrenfest urn model to complex networks, simulating random transport of conserved quantities. Mean-field theory accurately predicts system dynamics and equilibrium timescales across various network topologies.
Area of Science:
- Statistical Mechanics
- Network Science
- Complex Systems
Background:
- The Ehrenfest urn model describes particle distribution between two urns.
- Extending this model to complex networks is crucial for understanding transport phenomena.
Purpose of the Study:
- To generalize the Ehrenfest urn model to complex directed networks.
- To analyze the transport of conserved quantities and system dynamics.
Main Methods:
- Stochastic simulations to model packet evolution in network nodes.
- Mean-field theory to approximate ensemble-average behavior.
- Analysis of large scale-free and small-world networks.
Main Results:
- Mean-field approximation shows good agreement with simulations in the thermodynamic limit.
- Identified asymptotic dynamical states and timescales for equilibrium.
- Demonstrated the impact of network topology on system dynamics.
Conclusions:
- The generalized Ehrenfest urn model provides insights into transport in complex networks.
- Network connectivity and topology significantly influence system timescales.
- This framework aids in understanding real-world network responses to perturbations.
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