Adiabatic invariant

An adiabatic invariant is a physical quantity that remains constant during an adiabatic process. An adiabatic process is a thermodynamic process in which a system changes its internal energy without gaining or losing heat.

One of the most well-known adiabatic invariants is the action, a measure of the phase space volume occupied by a system. Action is conserved in adiabatic processes for systems with a large number of degrees of freedom and is related to the energy of the system.

Another important adiabatic invariant is the angular momentum, which is conserved during adiabatic processes for isolated systems. This means that the total angular momentum of a system is the same before and after an adiabatic process, even though the individual angular momenta of its components may change.

Adiabatic invariants play a key role in a variety of physical systems, including celestial mechanics, quantum mechanics, and plasma physics. They are used to describe the behavior of systems undergoing adiabatic processes and to predict their future states based on their initial conditions.

In general, adiabatic invariants are useful for understanding the behavior of physical systems under different conditions and for predicting the outcome of processes that occur over long periods of time. They provide a powerful tool for making quantitative predictions about the behavior of complex systems and are an important area of study in physics and engineering.