The Langevin Equation is a stochastic differential equation used to describe the evolution of a system subject to both deterministic and random forces, often used to model the dynamics of particles in a fluid. It incorporates both frictional and random forces, making it a cornerstone in the study of Brownian motion and non-equilibrium statistical mechanics.

Langevin Equation

stochastic differential equation

Deterministic forces

random forces

dynamics of particles

Fluid dynamics is a branch of physics that studies the behavior of fluids (liquids and gases) in motion and the forces acting on them. It is essential for understanding natural phenomena and designing systems in engineering disciplines, including aerodynamics, hydrodynamics, and meteorology.

Fluid Dynamics

Frictional forces are resistive forces that occur when two surfaces interact, opposing the relative motion or tendency of such motion between them. These forces are crucial in everyday life, providing the necessary grip for walking and driving, while also contributing to energy dissipation in mechanical systems.

Frictional Forces

Brownian motion is the random movement of particles suspended in a fluid, resulting from their collision with the fast-moving molecules in the fluid. It is a fundamental concept in statistical physics and serves as a mathematical model for stochastic processes, with applications in fields such as finance, biology, and physics.

Brownian motion

Non-equilibrium Statistical Mechanics is a branch of physics that studies systems not in thermodynamic equilibrium, focusing on how they evolve over time and approach equilibrium. It is crucial for understanding real-world processes where systems are driven by external forces, leading to phenomena such as transport processes, phase transitions, and fluctuations far from equilibrium.

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