Stochastic processes in physics, chemistry, and biology

The theory of stochastic processes emerged from efforts to quantitatively describe Brownian motion and has evolved into a powerful toolkit for analyzing the impact of noise across various systems. Key contributions from physicists and mathematicians such as Einstein, Smoluchowski, Langevin, Wiener, and Stratonovich have shaped its development. Traditionally, research in this field focused on mathematical and physical questions. However, recent years have seen significant advancements in applying stochastic methods to other sciences, particularly chemistry and biology. This surge in interest may stem from the growing recognition that noise can have a constructive role, rather than merely a detrimental one, in various processes. Beyond their theoretical appeal, noise-induced effects provide insights into unresolved issues, such as information transmission in the nervous system and cellular processes, including enzymatic reactions. Additionally, these concepts may lead to innovative technological applications, such as noise-enhanced reaction rates and transport mechanisms at the nanoscale. Important topics in this context include stochastic resonance, Brownian motors, and noise-supported phenomena in excitable systems.