The Liouville Equation

The Liouville equation describes how the distribution of particles in a system evolves over time in phase space, which combines their positions and momenta. It states that, in the absence of external influences, the total amount of particles within any region of phase space remains constant as particles move according to the laws of physics. Think of it like a map showing where particles are and how fast they’re going; the equation ensures this 'map' doesn't change shape over time, only redistributes, maintaining the overall 'density' of particles in phase space.