# Entropy, specific heat, susceptibility, and Rushbrooke inequality in percolation.

@article{Hassan2017EntropySH, title={Entropy, specific heat, susceptibility, and Rushbrooke inequality in percolation.}, author={M. Kamrul Hassan and D Alam and Zahidul Islam Jitu and M. M. Rahman}, journal={Physical review. E}, year={2017}, volume={96 5-1}, pages={ 050101 } }

We investigate percolation, a probabilistic model for continuous phase transition, 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. In addition, specific heat, OP, and susceptibility exhibit power law when approaching the critical point and the corresponding critical exponents α,β,γ respectably obey the Rushbrooke inequality (RI) α+2β+γ≥2. Their analogs in percolation, however…

## 6 Citations

### Product-sum universality and Rushbrooke inequality in explosive percolation.

- PhysicsPhysical review. E
- 2018

Explosive percolation on an Erdös-Rényi network for product rule (PR) and sum rule (SR) is studied and it is found that both PR and SR belong to the same universality class and obey Rushbrooke inequality.

### Redefinition of site percolation in light of entropy and the second law of thermodynamics.

- MathematicsPhysical review. E
- 2019

This article revisits random site and bond percolation in a square lattice with a focus on the behavior of entropy and the order parameter, and proposes an alternative definition for sitePercolation where the authors occupy sites to connect bonds and measure cluster size by the number of bonds connected by occupied sites.

### Universality class of explosive percolation in Barabási-Albert networks

- Materials ScienceScientific Reports
- 2019

This work study explosive percolation in Barabási-Albert network, in which nodes are born with degree k = m, for both product rule (PR) and sum rule (SR) of the Achlioptas process finds that the critical exponents ν, α, β and γ for m > 1 are found to be independent not only of the value of m but also of PR and SR.

### Precise bond percolation thresholds on several four-dimensional lattices

- PhysicsPhysical Review Research
- 2020

We study bond percolation on several four-dimensional (4D) lattices, including the simple (hyper) cubic (SC), the SC with combinations of nearest neighbors and second nearest neighbors (SC-NN+2NN),…

### Bond percolation between k separated points on a square lattice.

- MathematicsPhysical review. E
- 2020

We consider a percolation process in which k points separated by a distance proportional the system size L simultaneously connect together (k>1), or a single point at the center of a system connects…

### Observation of the magnetic criticality and the magnetocaloric effect in LaMn2Si2 in the vicinity of the phase transition around the room temperature

- Materials Science, PhysicsPhysics Letters A
- 2021

## References

SHOWING 1-5 OF 5 REFERENCES

### Introduction To Percolation Theory

- Physics
- 1985

Preface to the Second Edition Preface to the First Edition Introduction: Forest Fires, Fractal Oil Fields, and Diffusion What is percolation? Forest fires Oil fields and fractals Diffusion in…

### Introduction to Phase Transitions and Critical Phenomena

- Economics
- 1972

H E Stanley Oxford: University Press 1971 pp xx + 308 price ?5 In the past fifteen years or so there has been a lot of experimental and theoretical work on the nature of critical phenomena in the…

### Chaos

- HistoryMolecular Vibrations
- 2018

or "What a lie", or "How could I have said so"? or demanded at once that she should be sent for. Yet, he never on one single occasion, before others, spoke to Mrs. Cox on the subject. The only…

### and N

- I. Pavel, New Journal of Physics 12 093045
- 2010

### A: Math

- Gen. 9 L137
- 1976