Dynamical Systems

Dynamical systems study how things change over time according to specific rules. In Hamiltonian mechanics, they describe the movement of particles based on energy. In statistical mechanics, they analyze the collective behavior of many particles to understand temperature and pressure. Non-equilibrium thermodynamics examines systems not in balance, like engines or biological processes. Overall, dynamical systems use mathematics, like calculus, to model real-world phenomena, helping us predict how systems evolve and interact, whether in physics, biology, or engineering. They reveal the underlying patterns governing the dynamics of everything from simple motions to complex interactions.