Noncommutative probability is a branch of mathematics that extends traditional probability theory to settings where the order of events matters. In classical probability, the outcome of one event does not depend on the order of other events. However, in noncommutative probability, the relationships between events can be influenced by their sequence, making it useful in fields like quantum mechanics and statistical mechanics. This framework often employs concepts from operator algebra and quantum theory, where random variables are represented as noncommuting operators. This allows for a richer structure to model complex systems, capturing phenomena that classical probability cannot, such as the behavior of particles at the quantum level.