Electron Conductance Models Using Maximal Entropy Random Walks

We use thermodynamic models for systems for which we have incomplete information. These models are based on theorems such as the maximum uncertainty principle, which states that we should choose the scenario which maximizes the entropy of the statistical ensemble.

To model the behavior of particles plotted on a lattice, we usually use simplified models, which maximize the entropy locally: for each vertex, assume uniform probability among the possible outgoing edges: generic random walk (GRW). By considering a lattice with defects and adding a potential gradient, we can simulate classical electron conductance models.

Recently introduced models maximize entropy among possible stochastic processes, assuming a uniform distribution among possible paths: maximal entropy random walk (MERW). This leads to completely different stationary probabilistic densities, just as for the corresponding quantum ground state. This is expected also from quantum statistical thermodynamics and should give better approximations for nanoscale current flow.

This Demonstration enables you to compare stationary and dynamical behavior for both models in 2D, for various defect densities and potential gradients.