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Quantifying Disorder through Conditional Entropy: An Application to Fluid Mixing

Figure 1

Entropy of the Ising model.

Entropy per particle for the Ising model on a square lattice as a function of the temperature . (A) Glauber Dynamics (200×200 lattice). (B) Kawasaki dynamics with fixed zero magnetisation (100×100 lattice). We estimated from equilibrium ensembles of Monte-Carlo simulations using different approximations: mean field, Kikuchi and conditional entropy. In (A) we also compare our results with the exact solution obtained by Onsager [2]. The neighbourhood in is defined as the set of lattice sites within a maximum distance and in the upper half-plane from each site.

Figure 1