Recent Studies on Fokker–Planck Equation and Diffusion

Dear Colleagues,

Robert Brown's experiments concerning the irregular motion of small pollen grains suspended in water were essential to understanding one of the most fascinating fields of science—diffusion—in terms of the particles' random motion. With elegant arguments, the pioneering works of Einstein and Langevin have shown how it is possible to model this phenomenon. These works were followed by the essential contributions of Smoluchowski, Fokker, Planck, and others, which started a new field of research, namely, the stochastic process, in which diffusion is a specific type of stochastic process. Diffusion may be connected to Markovian or non-Markovian processes. The first is characterized by a linear dependence on the mean square displacement, and the second has a nonlinear displacement for the second moment. Different approaches have been successfully employed in analyzing the phenomena connected with the processes, such as continuous-time random walks, Langevin and Fokker–Planck equations, and extensions by incorporating fractional differential operators or nonlinear terms. Consequently, many aspects have been reported in different contexts in various fields of science, ranging from physics and engineering to biology.

We invite scholars to contribute to this Special Issue in the exciting field of stochastic processes. Contributions may include studies on diffusion (usual or anomalous), Fokker–Planck equations and extensions with fractional differential operators or nonlinear terms, continuous-time random walks, Schrödinger equations and extensions, etc.

Prof. Dr. Ervin K. Lenzi
Prof. Dr. Rafael Soares Zola
Prof. Dr. Haroldo Valentin Ribeiro
Guest Editors

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• diffusion
• Fokker–Planck equations
• continuous-time random walk
• Langevin equations
• fractional dynamics
• anomalous diffusion
• stochastic resetting
• comb model
• ergodicity
• Markovian processes
• non-Markovian processes
• nonequilibrium processes
• phase transitions
• nonequilibrium fluctuation theorems
• fluctuation-induced phenomena
• transport