xepma said:I'm not too familiar with this field (at all actually), but some books that seem to get reasonable reviews are:
Lemons (introductory):
https://www.amazon.com/dp/080186867X/?tag=pfamazon01-20
Reichl (more advanced, but not that well-written)
https://www.amazon.com/dp/3527407820/?tag=pfamazon01-20
Michael Plischke, Birger Bergersen (Reasonable book; has a chapter on stochastic processes, but covers a lot more than that)
https://www.amazon.com/dp/9812561552/?tag=pfamazon01-20
Cheers.
Brownian motion is the random movement of particles suspended in a fluid, caused by collisions with molecules in the fluid. It was first observed by botanist Robert Brown in 1827 and has since been studied extensively in the field of statistical mechanics.
Statistical mechanics helps us understand the behavior of systems made up of a large number of particles, such as gases, liquids, and solids. It provides a framework for predicting and explaining macroscopic properties from the microscopic behavior of individual particles.
Some popular books on statistical mechanics include "An Introduction to Statistical Mechanics" by Terrell L. Hill, "Statistical Mechanics: A Set of Lectures" by Richard P. Feynman, "Thermal Physics" by Daniel V. Schroeder, and "Statistical Mechanics: Entropy, Order Parameters and Complexity" by James P. Sethna.
Understanding Brownian motion has many practical applications, such as in the design of drug delivery systems, the development of new materials, and the study of diffusion in biological systems. It is also crucial in fields such as chemical engineering, nanotechnology, and biophysics.
While some knowledge of mathematics, particularly calculus and probability theory, is helpful in understanding Brownian motion and statistical mechanics, many books on the subject are written in a way that is accessible to a wide audience. It is possible to gain a basic understanding of these concepts without a strong background in advanced mathematics.