Abstract: Dr. Duda will introduce to Maximal Entropy Random Walk (MERW) chosen accordingly to the maximal entropy principle, which is crucial for statistical physics models. Standard diffusion uses local approximation of entropy maximization instead, leading to disagreement with quantum stationary probability distribution, e.g. incorrectly predicting nearly uniform electron density for semiconductor, what would make it a conductor. In contrast, MERW predicts (Anderson) localized densities in agreement with QM, what prevents conductance, e.g. allowing for model of diode as p-n junction (arXiv:2112.12557) - with electron diffusion easy only in one direction. While MERW assumes Boltzmann ensemble among all paths, I will also discuss ensemble of smooth paths instead by Langevin-like random walk in phase space (arXiv:2401.01239) e.g. to model tunneling, and surprisingly leading to slightly different stationary probability distribution (from phase space Schrödinger equation) - ability to gain velocity makes it easier to approach barriers, what might be crucial for molecular dynamics simulations.
Jarek Duda is an assistant professor at Jagiellonian University. He holds degrees in computer science (PhD), mathematics (MSc) and physics (PhD). He is mainly focused on physics foundations, information theory, statistical analysis, and is known for introduction of asymmetric numeral systems.
