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Dynamic Equilibrium02:20

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A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
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Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
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Published on: December 7, 2021

Duality between equilibrium and growing networks.

Dmitri Krioukov1, Massimo Ostilli

  • 1Cooperative Association for Internet Data Analysis, University of California San Diego, La Jolla, California 92093, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 17, 2013
PubMed
Summary
This summary is machine-generated.

Researchers demonstrate an exact equilibrium formulation for any growing network model, bridging equilibrium and nonequilibrium physics. This equivalence holds for finite systems, applicable to random geometric graphs, causal sets, and real-world networks.

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Analyzing the Size, Shape, and Directionality of Networks of Coupled Astrocytes
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Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
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Area of Science:

  • Statistical Physics
  • Network Science
  • Complex Systems

Background:

  • Networks can be modeled as either equilibrium or growing systems.
  • A clear distinction between equilibrium and nonequilibrium network models is often maintained.

Purpose of the Study:

  • To establish an equilibrium formulation for growing network models.
  • To demonstrate the equivalence between equilibrium and nonequilibrium network formulations.
  • To identify conditions under which this equivalence holds.

Main Methods:

  • Theoretical analysis of network models.
  • Investigating the conditions for equilibrium formulation in growing networks.
  • Comparing equilibrium and nonequilibrium formulations for finite system sizes.

Main Results:

  • An equilibrium formulation exists for any growing network model under specific conditions.
  • This equivalence between equilibrium and nonequilibrium formulations is exact for finite system sizes.
  • The conditions are met in random geometric graphs, causal sets, and some real networks.

Conclusions:

  • Growing network models can be precisely described using equilibrium formulations.
  • The established equivalence provides a unified framework for network analysis.
  • Findings have implications for understanding diverse network structures in physics and reality.