Thermodynamic analysis of diverse percolation transitions

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.