Thermodynamic analysis of diverse percolation transitions

TL;DR

This paper applies thermodynamic analysis to explosive and hybrid percolation models, revealing that entropy behaviors differ between continuous and discontinuous transitions, with implications for understanding phase transitions.

Contribution

It extends thermodynamic analysis to explosive and hybrid percolation, demonstrating the applicability of critical exponents and entropy behavior in these models.

Findings

Rushbrooke inequality holds as equality in both models

Entropy decreases continuously in explosive percolation

Entropy decreases discontinuously in hybrid percolation

Abstract

This work extends the thermodynamic analysis of random bond percolation to explosive and hybrid percolation models. We show that this thermodynamic analysis is well applicable to both explosive and hybrid percolation models by using the critical exponents $\alpha$ and $\delta$ obtained from scaling relations with previously measured values of $\beta$ and $\gamma$ within the error range. As a result, Rushbrooke inequality holds as an equality, $\alpha + 2\beta + \gamma = 2$, in both explosive and hybrid percolation models, where $\alpha > 0$ leads to the divergence of specific heats at the critical points. Remarkably, entropy clearly reveals a continuous decrease even in a finite-sized explosive percolation model, unlike the order parameter. In contrast, entropy decreases discontinuously during a discontinuous transition in a hybrid percolation model, resembling the heat outflow during discontinuous transitions in thermal systems.