Asymptotic entropy of the Gibbs state of complex networks

Abstract

In this work we study the entropy of the Gibbs state corresponding to a graph. The Gibbs state is obtained from the Laplacian, normalized Laplacian or adjacency matrices associated with a graph. We calculated the entropy of the Gibbs state for a few classes of graphs and studied their behavior with changing graph order and temperature. We illustrate our analytical results with numerical simulations for Erdős-Rényi, Watts-Strogatz, Barabási-Albert and Chung-Lu graph models and a few real-world graphs. Our results show that the behavior of Gibbs entropy as a function of the temperature differs for a choice of real networks when compared to the random Erdős-Rényi graphs.

References in corpus (4)

• Spatial search by quantum walk
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• Enhancing transport properties in interconnected systems without altering their structure
• Thermal state entanglement entropy on a quantum graph

Cited by in corpus (1)

• Lightcone Bounds for Quantum Circuit Mapping via Uncomplexity