Steady-state equilibrium and nonequilibrium noisy network dynamics

Area of Science:

• Theoretical physics
• Network science
• Statistical mechanics

Background:

• Networks often exhibit complex dynamics influenced by noise.
• Understanding nonequilibrium steady state (NESS) is crucial for many physical systems.
• Conventional Brownian dynamics models specific physical scenarios.

Purpose of the Study:

• To theoretically investigate fluctuating network dynamics around a stable state.
• To identify causes of nonequilibrium dynamics based on network properties and noise.
• To analyze NESS dynamics and derive a general fluctuation-dissipation relation.

Main Methods:

• Analysis of network connection properties and symmetry.
• Investigation of noise covariance matrices.
• Derivation of conditions for noisy network equilibrium.
• Analysis of steady-state probability current and drift velocity.
• Linearized fluctuating noisy network dynamics.

Main Results:

• Identified causes of nonequilibrium dynamics in networks.
• Derived equivalent conditions for noisy network equilibrium.
• Demonstrated overdamped Brownian dynamics as a special case of NESS.
• Derived a general fluctuation-dissipation relation for nonequilibrium noisy networks.
• Validated theoretical findings through numerical simulations.

Conclusions:

• The study provides a general framework for analyzing noisy directed networks in NESS.
• Overdamped Brownian dynamics is a specific instance within this broader framework.
• The derived fluctuation-dissipation relation offers new insights into energy dissipation in nonequilibrium systems.