On entropy, specific heat, susceptibility and Rushbrooke inequality in percolation

Abstract

We investigate percolation, a probabilistic model for continuous phase transition (CPT), on square and weighted planar stochastic lattices. In its thermal counterpart, entropy is minimally low where order parameter (OP) is maximally high and vice versa. Besides, specific heat, OP and susceptibility exhibit power-law when approaching the critical point and the corresponding critical exponents $\alpha, \beta, \gamma$ respectably obey the Rushbrooke inequality (RI) $\alpha+2\beta+\gamma\geq 2$. Their analogues in percolation, however, remain elusive. We define entropy, specific heat and redefine susceptibility for percolation and show that they behave exactly in the same way as their thermal counterpart. We also show that RI holds for both the lattices albeit they belong to different universality classes.