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) $\alpha +2\beta +\gamma \ge 2$. 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.

arXiv comment5 pages, 3 captioned figures, to appear as a Rapid Communication in Physical Review E, 2017

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Cited by in corpus (6)

• Precise bond percolation thresholds on several four-dimensional lattices
• Product-Sum universality and Rushbrooke inequality in explosive percolation
• Scaling behavior of information entropy in explosive percolation transitions
• Redefinition of site percolation in light of entropy and the second law of thermodynamics
• Universality class of explosive percolation in Barabási-Albert networks
• Thermodynamic analysis of diverse percolation transitions