Entropic equation of state and scaling functions near the critical point in scale-free networks

TL;DR

This paper derives scaling functions for entropy and related thermodynamic quantities near the critical point in scale-free networks, highlighting the role of the node-degree distribution exponent in critical phenomena.

Contribution

It extends the universality principle to scale-free networks by providing general scaling functions that incorporate the network's degree exponent.

Findings

Derived scaling functions for entropy and heat capacity near criticality.

Identified the node-degree exponent as a key variable influencing critical behavior.

Extended universality concepts to complex network structures.

Abstract

We analyze the entropic equation of state for a many-particle interacting system in a scale-free network. The analysis is performed in terms of scaling functions which are of fundamental interest in the theory of critical phenomena and have previously been theoretically and experimentally explored in the context of various magnetic, fluid, and superconducting systems in two and three dimensions. Here, we obtain general scaling functions for the entropy, the constant-field heat capacity, and the isothermal magnetocaloric coefficient near the critical point in scale-free networks, where the node-degree distribution exponent $\lambda$ appears to be a global variable and plays a crucial role, similar to the dimensionality $d$ for systems on lattices. This extends the principle of universality to systems on scale-free networks and allows quantification of the impact of fluctuations in the network structure on critical behavior.