Learn about the 3 most common types of stochastic processes in physics: Brownian motion, quantum mechanics, and thermodynamics.

3 Most Common Types of Stochastic Processes in Physics

Stochastic processes are mathematical models that describe the evolution of systems that are subject to random fluctuations. They are used to analyze a wide range of phenomena in physics, such as Brownian motion, quantum mechanics, and thermodynamics. In this article, we will discuss the three most common types of stochastic processes in physics.

1. Brownian Motion

Brownian motion is a type of stochastic process that describes the random movement of particles in a fluid or gas. It was first observed by the botanist Robert Brown in 1827, who noticed that pollen grains suspended in water exhibited a jittery, random motion.

The mathematical description of Brownian motion is given by the Langevin equation, which describes the motion of a particle subject to random forces. The Langevin equation is a stochastic differential equation that relates the velocity of the particle to the forces acting on it. The random forces are modeled as a Wiener process, which is a type of stochastic process that has independent, normally distributed increments.

Brownian motion has many applications in physics, such as in the study of diffusion processes, the behavior of polymers, and the dynamics of financial markets.

2. Quantum Mechanics

Quantum mechanics is the branch of physics that studies the behavior of particles on a very small scale, such as atoms and subatomic particles. In quantum mechanics, the evolution of a system is described by a wave function, which is a mathematical object that contains all the information about the system.

Stochastic processes are used in quantum mechanics to describe the random nature of measurements. When a measurement is made on a quantum system, the outcome is